Question

You have two identical solid objects (same mass mand specific heat c).They differ only in that one is at a temperature TH0= 450 K and the other at TC0=200 K.There is no phase transition between these two temperatures. You run a heat engine between themuntil they are both at the same final temperature.To do the maximum amount of work, what would be that final temperature?

Answer 1

final temperature is 300K

Step-by-step explanation:

Given data

temperature TH0 = 450 K

temperature TC0 = 200 K

to find out

final temperature

solution

we consider TH id temperature of hot and TC is temperature of cold object

so

dQH = -mc dTH ..........1

dQC = mc dTC ............2

and for max work

dQH/ TH = dQC/TC

put 1 and 2 here

-mc dTH / TH = mc dTC/ TC

now integrate both side from 450 to T and 250 to T

`\int_(450)^(T)-dTH/TH` =
`\int_(200)^(T)-dTC/TC`

we get ln 450/T = ln T/200

so Temp = √(450*200)

Temp = 300K

final temperature is 300K