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1 Physics -- First Law of Thermodynamics

105 calories of heat is required to raise the temperature of 3 moles of ideal gas at constant pressure from 25 C to 30 C. calculate the amount of heat required to raise the temperature of same gas through the same range of temperature at constant volume.

105 calories of heat is required to raise the temperature of 3 moles of ideal gas at constant pressure from 25 C to 30 C. calculate the amount of heat required to raise the temperature of same gas through the same range of temperature at constant volume.

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Solution:

Given,

(dQ)P = 105 calories

no of moles (n) = 3

initial temperature (T1) = 25 + 273 = 298 K

final temperature (T2) = 30 + 273 = 303 K

change in temperature (dT) = 303 - 298 = 15 K

We know,

Cp = (dQ)P / n'dT'

= (105 * 4.2) / (3 * 15)

= (9.8)

And,

Cp - Cv = R

or, (9.8) - (8.31) = Cv

So, Cv = 1.5

Now,

Let (dQ)v be the amount of heat required to raise the temperature of the gas through same difference at constant difference then,

(dQ)v = nCvdT

= (3 * 1.5 * 15)

= 67.5 J

= 16.07 cal

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