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Vadim26 [7]
4 years ago
8

Your research group has developed a new type of engine, which is now undergoing laboratory tests. In the engine, a sample of an

ideal gas with specific heat ratio γ is confined to a cylinder and carried through a closed cycle. The gas initially has pressure Pi, volume Vi, and temperature Ti. Its pressure is then tripled under constant volume. Then, it expands adiabatically to its original pressure. Finally, the gas is compressed isobarically to its original volume. What is the net work done by the engine for each cycle? (Use any variable or symbol stated above as necessary.)
Physics
1 answer:
Sunny_sXe [5.5K]4 years ago
6 0

Answer:

Explanation:

As we know that at isochoric conditions if pressure of the gas is tripled then the temperature also becomes 3 times

So heat given in this process is given as

Q_1 = nC_v\Delta T

Q_1 = n(\frac{R}{\gamma - 1})(3T_i - T_i)

Q_1 = \frac{2P_iV_i}{\gamma - 1}

Now it is expanded to initial pressure again by adiabatic process

So in this part there is no heat exchange

Q_2 = 0

Also we know that

(3P_i)^{1 - \gamma} (3T_i)^{\gamma} = (P_i)^{1 - \gamma}(T^{\gamma})

T = (3T_i)3^{\frac{1 - \gamma}{\gamma} = 3^{1/ \gamma}T_i

Now in the last process we compressed the gas to original volume

Q_3 = nC_p\Delta T

Q_3 = n(\frac{\gamma R}{\gamma - 1})(3^{1/ \gamma} T_i - T_i)

Q_3 = (\frac{\gamma R}{\gamma - 1})(3^{1 / \gamma} - 1)P_i V_i

Now total heat in the process is given as

Q = Q_1 + Q_2 + Q_3

Q = \frac{2P_iV_i}{\gamma - 1} + (\frac{\gamma R}{\gamma - 1})(3^{1 / \gamma} - 1)P_i V_i

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