Question

The specific heat of hydrogen gas at constant pressure is $C_{P} = 3.4 \times 10^{3}cal/kg^{o}C$and at constant volume is $C_{V} = 2.4 \times 10^{3}cal/kg^{o}C.$ If one kilogram hydrogen gas is heated from $10^{o}C$ to $20^{o}C$ at constant pressure, the external work done on the gas to maintain it at constant pressure is

• A. $10^{5}$cal
• B. $10^{4}$cal
• C. $10^{3}$ cal
• D. $5 \times 10^{3}$cal

Answer 1

Answer: (B)

$10^{4}$cal

Answer 2

From FLOT

∆Q = ∆U + ∆W

Work done at constant pressure

$(\Delta W)_{P} = (\Delta Q)_{P} - \Delta U$

$(\Delta Q)_{P} - (\Delta Q)_{V}$ (As we know $(\Delta Q)_{V} = \Delta U$)

Also $(\Delta Q)_{P} = mc_{P}\Delta T$ and $(\Delta Q)_{V} = mc_{V}\Delta T$

⇒ $(\Delta W)_{P} = m(c_{P} - c_{V})\Delta T$

⇒ $(\Delta W)_{P} = 1 \times (3.4 \times 10^{3} - 2.4 \times 10^{3}) \times 10 = 10^{4}cal$