A piston contains 320 moles of an ideal monatomic gas that initially has a press

Question

A piston contains 320 moles of an ideal monatomic gas that initially has a pressure of 2.29 times 10^5 Pa and a volume of 1.8 m^3 The piston is connected to a ho: and cold reservoir and the gas goes through the following quasi-static cycle accepting energy from the hot reservoir are exhausting energy into the cold reservoir. The pressure of the gas is increased to 5.29 times 10^5 Pa while maintaining a constant volume. The volume of the gas is increased to 8.8 m^3 while maintaining a constant pressure. The pressure of the gas is decreased to 2.29 times 10^5 Pa while maintaining a constant volume. The volume of the gas is decreased to 1.8 m^3 while maintaining a constant pressure. It may help you to recall that C_v - 12.47 J/K/mole and C_p - 20.79 J/K/mole for a monatomic ideal gas. and that the number of gas molecules is equal to Avogadro's number (6.022 times 10^23) times the number of moles of the gas. How much energy is transferred into the gas from the hot reservoir? You c

Explanation / Answer

The change of base formula for logarithmic operations, if x > 0 and a 1, b 1, is logb(x)=loga(x)/loga(b).

Here, let b = 1/3, x = 6 and a = 10. Then log1/3 6 = log10(6)/log10(1/3) = log10(6)/[ log10 1- log10 3] = 0.77815125/(0- 0.477121254) = - 0.77815125/0.477121254 = - 0.163092975 = -0.16 ( on rounding off to 2 decimal places).

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