In a steam engine the pressure and volume of steam satisfy the equation $P V^{1.4}=k$ , where k is a constant. (This is true for adiabatic expansion, that is, expansion in which there is no heat transfer between the cylinder and its surroundings.) Calculate the work done by the engine (in ft-lb) during a cycle when the steam starts at a pressure of $160 \mathrm{~lb} / \mathrm{in}^{2}$ and a volume of $100 \mathrm{~in}^{3}$ and expands to a volume of $800 \mathrm{~in}^{3} .$ Use the fact that the work done by the gas when the volume expands from $V_{1}$ to volume $V_{2}$ is $W=\int_{V_{1}}^{V_{2}} P d V$ .

Question

In a steam engine the pressure and volume of steam satisfy the equation

P V^{1.4}=k

, where k is a constant. (This is true for adiabatic expansion, that is, expansion in which there is no heat transfer between the cylinder and its surroundings.) Calculate the work done by the engine (in ft-lb) during a cycle when the steam starts at a pressure of

160 \mathrm{~lb} / \mathrm{in}^{2}

and a volume of

100 \mathrm{~in}^{3}

and expands to a volume of

800 \mathrm{~in}^{3} .

Use the fact that the work done by the gas when the volume expands from

V_{1}

to volume

V_{2}

is

W=\int_{V_{1}}^{V_{2}} P d V

.

Quizplus · Accepted Answer

The Answer of In a steam engine the pressure and volume of steam satisfy the equation $P V^{1.4}=k$ , where k is a constant. (This is true for adiabatic expansion, that is, expansion in which there is no heat transfer between the cylinder and its surroundings.) Calculate the work done by the engine (in ft-lb) during a cycle when the steam starts at a pressure of $160 \mathrm{~lb} / \mathrm{in}^{2}$ and a volume of $100 \mathrm{~in}^{3}$ and expands to a volume of $800 \mathrm{~in}^{3} .$ Use the fact that the work done by the gas when the volume expands from $V_{1}$ to volume $V_{2}$ is $W=\int_{V_{1}}^{V_{2}} P d V$ .

In a Steam Engine the Pressure and Volume of Steam PV1.4=kP V^{1.4}=kPV1.4=k

In a Steam Engine the Pressure and Volume of Steam $P V^{1.4}=k$