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                                    The ratio of the molar heat capacities of an ideal gas is `(C_p / C_v 7/6)`. Calculate the change in internal energy of 1.0mole of the gas when its temperature is raised by `50 k (a)` keeping the pressure constant , (b) keeping the volume constant and (c ) adiabatically. | 
                            
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Answer» `(C_p/C_V)=7/6`, `n=1 mol.`, `DeltaT=50 K` (a) Keeping the pressure constant, `dQ = dU + dW`, `DeltaT = 50 K, gamma =7/6`, `n=1 mol.` `dQ=dU=dW` `implies nC_pdT=dU+RdT` `dU=nC_pdT-RdT` `=1xx(Rgamma)/(gamma-1)xxdT-RdT` `=7Rdt - RdT` `=7Rdt-RdT=6RdT` `=6xx8.3xx50 = 2490J.` (b) Keeping volume constant, `dU=nC_vdT` `=1 xx R/(gamma-1) xxdT` `=1((8.3)/(7//6)-1)xx50 ` `=8.3 xx 50 xx 6 = 2590 J.` (c) Adiabatically, `dQ=0`, `dU=-dW` `=[(nxxR)/(gamma-1)(T_1-T_2)]` `=(1xx83)/(7//6-1)= (T_2-T_1)` `=8.3 xx 6 xx 50 = 2490 J`.  | 
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