Question

A heat engine with 0.500 mol of a monatomic ideal gas initially fills a 1000 cm3 cylinder at 700 K . The gas goes through the following closed cycle: - Isothermal expansion to 6000 cm3. - Isochoric cooling to 400 K . - Isothermal compression to 1000 cm3. - Isochoric heating to 700 K .

Answer 1

Answer:

2234.63

Explanation:

Work done per cycle by the engine is calculated as;

$W=\int p \ dv$

#Since volume doesn't change in the isochoric steps, there is no work done, hence:

$W_2=W_3=0$

#For an isothermal change of state(ideal gas):

$pV=nRT\\\\W=P_iV_ i\int \frac{1}{V} \ dV\\\\=P_iV_ iIn(V_f/V_i)$

#for the expansion process:

$W_i=0.5mol\times8.3145J/molK\times 700K \ In(6000cm^3/1000cm^3)\\\\W_i=5214.15J$

$W_4=0.5mol\times8.3145J/molK\times 400K \ In(6000cm^3/1000cm^3)\\\\W_4=-2979.52$

$W=W_1+W_2+W_3+W_4\\\\=5214.15J-2979.52\\\\=2234.63J$

Hence, the engine does 2234.63J per second.