• # question_answer 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

 [b] From FLOT DQ = DU + DW 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 ${{(\Delta Q)}_{V}}=m{{c}_{V}}\Delta T$ Þ ${{(\Delta W)}_{P}}=m({{c}_{P}}-{{c}_{V}})\Delta T$ Þ ${{(\Delta W)}_{P}}=1\times (3.4\times {{10}^{3}}-2.4\times {{10}^{3}})\times 10={{10}^{4}}cal$