40 calories of heat is needed to raise the temperature of 1, mole of an ideal monoatomic gas from 20°C to 30°C at a constant

Q: $40$ calories of heat is needed to raise the temperature of $1\, mole$ of an ideal monoatomic 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 $(R = 2\,calorie\,mol{e^{ - 1}}{K^{ - 1}})$ is ..... $calorie$

a At constant pressure, the amount of heat required is $Q = nC _{ p } \Delta T$ $40=1 \times C_{p} \times 10$ Thus, $C _{ p }=4$ Now, $\gamma=\frac{ C _{ p }}{ C _{ v }}$ $\gamma$ for monoatomic gas $=1.67$ Thus, $C _{v}=\frac{ C _{p}}{\gamma}=\frac{4}{1.67}=2.4$ For a constant volume process, $Q = nC _{ v } \Delta T$ Thus, $Q=1 \times 2.4 \times 10$ $Q =24 cal \approx 20 cal$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

$40$ calories of heat is needed to raise the temperature of $1\, mole$ of an ideal monoatomic 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 $(R = 2\,calorie\,mol{e^{ - 1}}{K^{ - 1}})$ is ..... $calorie$

A$20$
B$40$
C$60$
D$80$

Medium

STD 11 Science
JEE
STD 11 - 12 . kinetic theory of gases
Physics

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