Kinetic Theory Of Gases Question 158
Question: 40 calories of heat is needed to raise the temperature of 1 mol of an ideal monoatomic gas from $ 20{}^\circ C $ to $ 30{}^\circ C $ at a constant pressure. The amount of heat required to raise its temperature over the same interval at a constant volume (R = 2 cal/mol/K) is
Options:
A) 20 cal
B) 40 cal
C) 60 cal
D) 80 cal
Show Answer
Answer:
Correct Answer: A
Solution:
[a] At constant pressure $ {{(\Delta Q)}_p}=\mu C_p\Delta T=1\times C_p\times (30-20)=40 $
$ \Rightarrow C _{p}=4\frac{\text{calorie}}{\text{moke},\text{kelvin}} $
$ \
Therefore $ $ C _{v}=C _{p}-R=4-2=2,\frac{\text{calorie}}{\text{mole }\times\text{ kelvin}} $ Now,
$ {(\Delta Q)_v}=\mu C_v \Delta T $
$ =1\times 2\times (30-20) $
$ =20\text{cal} $
BETA
