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
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(b) From FLOT $\Delta Q = \Delta U + \Delta W$
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 ${(\Delta Q)_P} = m{c_P}\Delta T$ and ${(\Delta Q)_V} = m{c_V}\Delta T$
==> ${(\Delta W)_P} = m({c_P} - {c_V})\Delta T$
==> ${(\Delta W)_P} = 1 \times (3.4 \times {10^3} - 2.4 \times {10^3}) \times 10 = {10^4}cal$
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 ${(\Delta Q)_P} = m{c_P}\Delta T$ and ${(\Delta Q)_V} = m{c_V}\Delta T$
==> ${(\Delta W)_P} = m({c_P} - {c_V})\Delta T$
==> ${(\Delta W)_P} = 1 \times (3.4 \times {10^3} - 2.4 \times {10^3}) \times 10 = {10^4}cal$
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