1. Tardigrade
  2. Question
  3. Physics
  4. Forty calories of heat is needed to raise the temperature of 1 mol of an ideal monatomic gas from 20° C to 30° 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 -1 K -1) is

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Q. Forty calories of heat is needed to raise the temperature of $1 \,mol$ of an ideal monatomic 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 $\left(R=2 \,cal \,mol ^{-1} K ^{-1}\right)$ is

Kinetic Theory

Solution:

At constant pressure $Q_{p}=\mu C_{p} \Delta T$
$=1 \times C_{p} \times(30-20)=40 \,cal$
$\Rightarrow C_{p}=4 \,cal / mol - K$
$\therefore C_{v}=C_{p}-R=4-2=2 \,cal / mol - K$
Now $Q_{v}=\mu C_{v} \Delta T=1 \times 2 \times(30-20)=20 \,cal$