A carnot engine has 40 g of helium gas as its working substance. it operates bet

Question

A carnot engine has 40 g of helium gas as its working substance. it operates between two reservoirs of temperatures T1= 400 0C AND T2= 60 0C. The initial volume of the gas is V1= 2.0 X 10-2 m3, the volume after isothermal expansion is V2= 4.0 X 10-2 m3, and the volume after the subsequent adiabatic expansion is V3= 5.0 x 10-2m3. (a) calculate the work generated by this engine during one cycle. (b) calculate the heat absorbed and the waste heat ejected during one cycle. A carnot engine has 40 g of helium gas as its working substance. it operates between two reservoirs of temperatures T1= 400 0C AND T2= 60 0C. The initial volume of the gas is V1= 2.0 X 10-2 m3, the volume after isothermal expansion is V2= 4.0 X 10-2 m3, and the volume after the subsequent adiabatic expansion is V3= 5.0 x 10-2m3. (a) calculate the work generated by this engine during one cycle. (b) calculate the heat absorbed and the waste heat ejected during one cycle.

Explanation / Answer

Given T_1 = 40 ^ oC =313 k T_2 = 60 ^ oC   = 333 k V_1 =   2*10^ -2 m^ 3 V_2 =   4*10^ -2 m^3 V_3= 5.0 x 10^-2 m^3     work generated by heat engine             W = carnot efficiency *Q_H        where   Q_H   =   n c_v ( T_2 - T _1 )               carnot efficency                       = 1 - T_c / T_H number of moles   n = 40g / 4 g / mol    = 10 mol heat absorbed          Q =    n R T_H ( ln (   V_2 / V_1) plug the values and get the answers                                                              

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