Question

40 calories of heat is needed to raise the temperature of 1 mole of an ideal monoatomic gas from 20⁰C to 30⁰C at a constant pressure. The amount of heat required to raise its temperature over the same interval at a constant volume $(R = 2caloriemole^{- 1}K^{- 1})$ is

• A. 20 calorie
• B. 40 calorie
• C. 60 calorie
• D. 80 calorie

Answer 1

Answer: (A)

20 calorie

Answer 2

At constant pressure $(\Delta Q)_{p} = \mu C_{p}\Delta T$ $= 1 \times C_{p} \times (30 - 20) = 40$

⇒ $C_{p} = 4\frac{calorie}{molekelvin}$

∴ $C_{v} = C_{p} - R$ $= 4 - 2 = 2\frac{calorie}{mole \times kelvin}$

Now $(\Delta Q)_{v} = \mu C_{v}\Delta T = 1 \times 2 \times (30 - 20) = 20calorie$