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**1. Homework Statement**

Question 1) a mass m=200g or an unknown metal is heated to a temperature T1=200°C and then dropped into m=50g of water at a temperature T2=20°C in an insulated container. The water temperature rises within a few seconds to T3=39.7°C and then changes no further. Specific heat capacity of water=4190 J/kgK. Find the specific heat capacity of the metal cM.

Question 2) A small metal container holds water of a mass m=20g at a temperature T=20°C. Another large ridig container with Volume V=4000cm^3 holds n=0.4mol moles of monoatomoic gas at a pressure p1=10^6pa and a temperature T1. The metal container and the large container are placed in good thermal contact with each other. Both containers are perfectly insulated from the outside. The containers are left like this for a long time so thermal equilibirum is established. Specific heal of water is c=4186 J/Kg*K. Find the pressure p2 after the containers are in thermal equilibirum.

**2. Homework Equations**

Q=m*c*ΔT

pV=n*R*T

ΔEth=-W+Q

ΔEth=3/2*n*R*ΔT

p/T=constant

**3. The Attempt at a Solution**

I have the solutions for both problems but there is an aspect of the solutions which my understanding needs a great deal of improvement.

Question 1)

In this problem the heat energy in water (Qw) gains heat energy because when the hot metal is dropped in the water its heat is transffered to the water, so the hot metal loses energy (Qm)?

There for Qw = -Qm

Question 2)

In this problem there is a temperature difference between the water container and the gass container so we know there will be heat transfer. Since the calculated Temperature of the gas T1 is greater then the temperature of water T=20 it is said that the heat Q flows from the container to the water container so in other words if one object has greater temperature then the other heat will transfer from the high temp object to the low temp object?

Since heat will transfer from the gas container to the water, you'd think the water gains the energy and the gas loses the energy. So the heat energy of water (Qw) = -Q(heat energy of the gas)

But in the solution this is not the case and the heat energy of the gas Q = -Qw implying that the gas gains energy while the water loses energy.

Where am i going wrong in the questions? the prolems i have in them are very similar, i believed i have not read the scenarios correctly.

Any help great appreciated, thanks guys.