Solving Physics Problems: Specific Heat Capacity and Elastic Limit Explained"

[MatureS99]

Help needed, started my course late!

Hi everyone, I'm new to the forum and am wondering if anyone could answer these questions for me and explain them. I understand that it's very ignorant for this to be my first post, but would greatly appreciate it. Even if you can't or don't have the time to explain it, just the answers would be great...Thanks ?They're the only two I can't get.

i)4400 J of energy are used to heat a 1kg metal block by 16°C. What is the specific heat capacity of the metal?

ii) a 1.5kg aliminium kettle contains 1.5kg of water at 20°C. If the kettle element supplies 2000J/s, how long will it take to heat up 50 degrees ? (Specific heat capacity of aliminium = 900J/(kg°C) specific heat capacity of water is 4200J/(kg degree C)

2. A spring of natural length 15cm is stretched to 18cm when a mass of 50g is attached. (g=10m/s ²)

i) calculate the new length of of the spring if a mass of 225 g is attached (assuming the spring does not exceed its elastic limit). Also define the term elastic limit.

ii) Two such springs are used side-by-side to support the same 225 g mass, calculate the extension of each.

Many many thanks in advanced, I'm only back at education this year and everything is rusty.

I should also add that my physics teacher has been helping me get slowly and surely back into this, but he is off this week. These two questions are the only ones I can't get as there was a practical exam set out for both of them, and as previously said I started the course late and missed them. Many thanks in advanced.

 

[LawrenceC]

i)4400 J of energy are used to heat a 1kg metal block by 16°C. What is the specific heat capacity of the metal?

You are changing the temperature of the block. Its internal energy changes when this happens. Internal energy is generally given the symbol U where

U = m*Cv*T
and m is mass, Cv is specific heat, and T is temperature.

So if there is a change in temperature you can write

dU = m*Cv*(Tnew - Told)

The problem states the temperature change, the mass, and the energy input. The only unknown is the specific heat. Compute it.

ii) a 1.5kg aliminium kettle contains 1.5kg of water at 20°C. If the kettle element supplies 2000J/s, how long will it take to heat up 50 degrees ? (Specific heat capacity of aliminium = 900J/(kg°C) specific heat capacity of water is 4200J/(kg degree C)

This problem is similar except the energy input is given as a rate, Joules/second. Determine how long it takes to change the internal energy to what you need remembering U = m*Cv*T.

Always make sure your units jive. Units on left side of any equation must ALWAYS agree with units on the other side of equation. And things with unlike units cannot be added or subracted.

 

[MatureS99]

i)4400 J of energy are used to heat a 1kg metal block by 16°C. What is the specific heat capacity of the metal?

You are changing the temperature of the block. Its internal energy changes when this happens. Internal energy is generally given the symbol U where

U = m*Cv*T
and m is mass, Cv is specific heat, and T is temperature.

So if there is a change in temperature you can write

dU = m*Cv*(Tnew - Told)

The problem states the temperature change, the mass, and the energy input. The only unknown is the specific heat. Compute it.

ii) a 1.5kg aliminium kettle contains 1.5kg of water at 20°C. If the kettle element supplies 2000J/s, how long will it take to heat up 50 degrees ? (Specific heat capacity of aliminium = 900J/(kg°C) specific heat capacity of water is 4200J/(kg degree C)

This problem is similar except the energy input is given as a rate, Joules/second. Determine how long it takes to change the internal energy to what you need remembering U = m*Cv*T.

Always make sure your units jive. Units on left side of any equation must ALWAYS agree with units on the other side of equation. And things with unlike units cannot be added or subracted.

Thanks...You seem to be very intelligent :)

I need the actual answers(figures) though for my graph and table. If you could help it would be great, I'm currently wiriting down everything you just said though.

 

[LawrenceC]

With a spring, the force provided by a spring is

F = k*x where
F is force
k is spring constant
x is the compression or stretch of spring.

Units of k and x must be such that they provide units of force when multiplied. In your problem, you are given mass. Mass must be multiplied by the gravitational constant to provide force. Grams are mass not force.

 

[MatureS99]

With a spring, the force provided by a spring is

F = k*x where
F is force
k is spring constant
x is the compression or stretch of spring.

Units of k and x must be such that they provide units of force when multiplied. In your problem, you are given mass. Mass must be multiplied by the gravitational constant to provide force. Grams are mass not force.

Fantastic, thanks. God bless you, ha.

 

[LawrenceC]

"Thanks...You seem to be very intelligent :)"

I scrape by...

Just use your calculator. If dU = m*Cv*(Tnew-Told), then

Cv = dU/(m*(Tnew-Told))= 4400/(1*16)

The units are Joules/(kg-C)

 

[MatureS99]

I don't even know what that means*embarrassed*

 

[LawrenceC]

Exactly what don't you understand? What part of what I wrote?

 

[berkeman]

Hi everyone, I'm new to the forum and am wondering if anyone could answer these questions for me and explain them. I understand that it's very ignorant for this to be my first post, but would greatly appreciate it. Even if you can't or don't have the time to explain it, just the answers would be great...Thanks ?They're the only two I can't get.

i)4400 J of energy are used to heat a 1kg metal block by 16°C. What is the specific heat capacity of the metal?

ii) a 1.5kg aliminium kettle contains 1.5kg of water at 20°C. If the kettle element supplies 2000J/s, how long will it take to heat up 50 degrees ? (Specific heat capacity of aliminium = 900J/(kg°C) specific heat capacity of water is 4200J/(kg degree C)

2. A spring of natural length 15cm is stretched to 18cm when a mass of 50g is attached. (g=10m/s ²)

i) calculate the new length of of the spring if a mass of 225 g is attached (assuming the spring does not exceed its elastic limit). Also define the term elastic limit.

ii) Two such springs are used side-by-side to support the same 225 g mass, calculate the extension of each.

Many many thanks in advanced, I'm only back at education this year and everything is rusty.

I should also add that my physics teacher has been helping me get slowly and surely back into this, but he is off this week. These two questions are the only ones I can't get as there was a practical exam set out for both of them, and as previously said I started the course late and missed them. Many thanks in advanced.

It is against the PF rules for us to do your schoolwork for you. We may only provide hints...

 

[MatureS99]

It is against the PF rules for us to do your schoolwork for you. We may only provide hints...

Apologies, I didn't know this.

Lawrence I will update this when i get home, thanks.

 

[technician]

SPECIFIC heat capacity... the key word is SPECIFIC. It means 'per kilogram'
SHC is the amount of heat energy needed to change the temperature OF 1 kg by 1 degree C.
Water has an SHC of 4200 joules per kg per C. This is a large SHC and you could say that water can 'soak' up heat energy. This is why it is such a good coolant and also a good storer of heat energy.
In your question 4400 Joules of energy raise the temperature of 1kg of a metal by 16C.
The SHC of this metal is almost 16 times less than that of water
the main equation in this work is
Heat energy = mass x SHC x temp change
H = m x c x (t2 - t1)

 

[technician]

The 1.5kg aluminium kettle is heated from 20C to 50C...calculate how much energy is needed
The 1.5kg of water is heated from 20C to 50C... calculate the energy needed
Add the energies together.
Energy is supplied at 2000joules per second...how long does it take?

 

[technician]

The most important thing to know about a spring is the SPRING CONSTANT (also known as 'stiffness')
This is the FORCE needed to cause the spring to stretch by 1m. The unit is N/m
You have to be careful with units here... If you are told that a MASS (in kg or g) is hung on the spring you must find the FORCE (weight).
1kg weighs 9.81N. This is what 'g' means (sometimes it is rounded off to 10N for convenience)
In your question a mass of 50g (0.05kg) stretches a spring by 3cm (.03m)
The weight of 50g is therefore 0.05 x 9.81N = 0.49N
The spring constant of the spring is therefore 0.49/0.03 = 16N/m
You do not need to do this to do your question but it is the way to know when dealing with springs.
I hope this is useful.
Good luck, don't give up