Question

The specific heat of hydrogen gas at constant pressure is Cp = 6.4 x 10³ cal/kg °C and at constant volume is Cv = 4.4 x 10³ cal/kg °C. If one kilogram of hydrogen gas is heated from 10 °C to 20 °C at constant pressure, the external work done on the gas to maintain it at constant pressure is ______.

Options

• 20 x 10³ calories

• 10⁴ calories

• 10³ calories

• 5 x 10³ calories

Answer 1

The specific heat of hydrogen gas at constant pressure is Cp = 6.4 x 10³ cal/kg °C and at constant volume is Cv = 4.4 x 10³ cal/kg °C. If one kilogram of hydrogen gas is heated from 10 °C to 20 °C at constant pressure, the external work done on the gas to maintain it at constant pressure is 20 x 10³ calories.

Explanation:

From first law of thermodynamics,

Q= `Delta"U"`+ W

Work done at constant pressure,

`("w")_p=("Q")_p-Delta"U"`

`("w")_p=("Q")_p-(Delta"U")_v`   .....[∵ `("Q")_v=Delta"U"`

Also, `("Q")_p=mC_pDelta"T" and (Delta"Q")_v=mC_vDelta"T"`

∴ `("w")_p=m(C_p-C_v)Delta"T"`

∴`("w")_p=1xx(6.4xx10^3-4.4xx10^3)xx10`

=`20 xx 10^3 ` cal