First slide

Specific heat

Question

H calories of heat are required to raise the temperature of 1 mole of a monoatomic gas from 20°C to 30°C at constant volume, The amount of heat required (in calories) to raise the temperature of 2 moles of a diatomic gas from 20°C to 25°C at constant pressure is

Moderate

A

(4/3) H
B

(5/3) H
C

2 H
D

(7/3) H

Solution

$H = 1 \times C_{V} \times 10 and Q = 2 \times C_{p} \times 5 ∴ \frac{Q}{H} = 2 (C_{p} / C_{v}) \times \frac{1}{2} = (C_{p} / C_{v})$
For diatomic gas, C_p =(7/2) R. For monoatomic gas
$C_{V} = (3 / 2) R$
$∴ \frac{Q}{H} = \frac{(7 / 2) R}{(3 / 2) R} = \frac{7}{3} or Q = \frac{7}{3} H$

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