Can Wally Whacko's Heat Engine Truly Achieve 92% Efficiency?

[chipM]

Homework Statement

1)Wally whacko claims to have invented a heat engine that will revulutionalise the industry. It runs between a hot source at 300 C and a cold sink at 25 C . he claims that his engine is 92 % effieicnt.
What is the max efficiency of his engine ? in 2sf

(2)At a certain location the solar power per unit area reaching Earth suface is 200 w/m^2. Averaged over 24 hour day.
If the average requirement in your home is 3.8 kw and you can convert solar power to elevtric power with 10% efficiency, how large a collector area will you need to meet all your house hold energy requirement from solar energy.

(3)The soecific heat capacity of ice is about 0.5 cal/g C.
Suppose that it remains at that value all the way to absolute zero. Calculate the number of calories it would take to change a 0.90g ice cube at absolute zero ( -273 C) t 0.90 g of boiling water.
How does this number of calories compare with the number of calories required to change the same gram of 100 C boiling water to 100 C steam. ?

Homework Equations

1) t(h)-t(c)/ t(h)
i don't know number 2
3) q=mct

The Attempt at a Solution

1) 300-25 /300 = 91.667 so its 91.667% efficeint
2) idont know where to start
3) o.90 x -273 x 0.5= -122.850

are they right ? please correct me if i am wrong with proper working

thanks !

 

[SammyS]

Homework Statement

1)Wally whacko claims to have invented a heat engine that will revulutionalise the industry. It runs between a hot source at 300 C and a cold sink at 25 C . he claims that his engine is 92 % effieicnt.
What is the max efficiency of his engine ? in 2sf

(2)At a certain location the solar power per unit area reaching Earth suface is 200 w/m^2. Averaged over 24 hour day.
If the average requirement in your home is 3.8 kw and you can convert solar power to elevtric power with 10% efficiency, how large a collector area will you need to meet all your house hold energy requirement from solar energy.

(3)The soecific heat capacity of ice is about 0.5 cal/g C.
Suppose that it remains at that value all the way to absolute zero. Calculate the number of calories it would take to change a 0.90g ice cube at absolute zero ( -273 C) t 0.90 g of boiling water.
How does this number of calories compare with the number of calories required to change the same gram of 100 C boiling water to 100 C steam. ?

Homework Equations

1) t(h)-t(c)/ t(h)   What temperature scale is needed for this to be true?
i don't know number 2
3) q=mct

The Attempt at a Solution

1) 300-25 /300 = 91.667 so its 91.667% efficeint
2) [STRIKE]idont[/STRIKE] I don't know where to start    Oh please! This just requires some proportions and the cancelling of units.
3) o.90 x -273 x 0.5= -122.850

are they right ? please correct me if i am wrong with proper working

thanks !

Hello chipM. Welcome to PF !

None of your answers is correct.

For #3: Why the negative sign when the change in temperature is positive?

How many calories does it take to melt ice -- latent heat of fusion.

What is the specific heat capacity of liquid water?​

 

[chipM]

for liquid water its 4.18 i recon

i don't know about your other question though

how do i solve the other two questions ? please help me

thank you

 

[voko]

For #1, use absolute temperature scale (kelvins).

For #2, start by finding how much solar power a solar panel has to consume to produce 3.8 kW at 10% efficiency.

For #3, ice goes from -273 to 0, melts, and then goes to +100.

 

[chipM]

thanks mate

so i have to convert the temparature for 1) to kelvinss ?

so for 3) i got -173 x 0.09 x 0.5= -7.785 joules

correct ?

 

[SammyS]

thanks mate

so i have to convert the temperature for 1) to Kelvin ?

Yes, or °Rankine if you prefer.

 

[chipM]

Yes, or °Rankine if you prefer.

cheers :)

so for 3) i got -173 x 0.09 x 0.5= -7.785 joules

correct ?

 

[voko]

so for 3) i got -173 x 0.09 x 0.5= -7.785 joules

correct ?

Not even close. As I said, the ice goes through three distinct stages on its way from abs. zero to boiling water.

 

[SammyS]

cheers :)

so for 3) i got -173 x 0.09 x 0.5= -7.785 joules

correct ?

The temperature changes are positive. Why do you show it being negative again? This time, you seem to have ice going from -100°C to -273°C .

As voko pointed out:

For #3, ice goes from -273°C to 0°C, melts, and then goes to +100°C .​

 

[chipM]

The temperature changes are positive. Why do you show it being negative again? This time, you seem to have ice going from -100°C to -273°C .

As voko pointed out:

For #3, ice goes from -273°C to 0°C, melts, and then goes to +100°C .​

k i am working on 3)

for 1) is it (573.15- 298.15)/ 573.15 = 0.48

which means its only 48% efficient ?

 

[SammyS]

for 1) is it (573.15- 298.15)/ 573.15 = 0.48

which means its only 48% efficient ?

Yes.

 

[chipM]

The temperature changes are positive. Why do you show it being negative again? This time, you seem to have ice going from -100°C to -273°C .

As voko pointed out:

For #3, ice goes from -273°C to 0°C, melts, and then goes to +100°C .​

hey man i still don't get how to do 2)

so is the temparature change 373 ?

which mean its going to be

0.5x 0.009x 373 = 0.168 .

yes ?

 

[SammyS]

hey man i still don't get how to do 2)

You state that you don't know how to do 2, then jump right into #3 without mentioning that's what you're doing ?

so is the temperature change 373 ?

which mean its going to be

0.5x 0.009x 373 = 0.168 .

yes ?

No.

The temperature increase is 373°C, but the first 273 of that is for ice. (You do know that the ice melts at 0°C, right?)

How much heat does it take to melt 0.90 g of ice ?

Then the liquid water requires yet more heat to raise its temperature to the boiling point. (100°C at 1 atmosphere of pressure.) As I said before, the specific heat capacity of liquid water is different than that of ice. (Do you know what it is?)

After adding all that, how does that compare to the amount of heat required to change 0.90 g of liquid water to steam ?