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A 175 mm diameter cylinder contains 215 cm\(^3\) of water at 60°C. A 35 kg piston sits on top of the water. If heat is added until the temperature reaches 160°C, find the work done.

Answer :

Answer:

Explanation: work done, cylinder, water, piston, heat, temperature, ideal gas law

Final answer:

The work done on the piston when heat is added until the temperature is 160oC can be calculated using the ideal gas law and the equation for work done by a gas. By substituting the given values and solving the equations, the work done can be determined.

Explanation:

To calculate the work done on the piston, we need to use the ideal gas law and the equation for work done by a gas.

The ideal gas law is given by:

PV = nRT

Where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.

In this case, we have water in the cylinder, so we need to convert the volume of water to moles of water using the molar volume of water.

The molar volume of water is approximately 18 cm3/mol.

So, the number of moles of water is:

n = V / molar volume

Substituting the given values:

n = 215 cm3 / 18 cm3/mol

Now, we can calculate the initial pressure using the ideal gas law:

Pi * Vi = n * R * Ti

Where Pi is the initial pressure, Vi is the initial volume, Ti is the initial temperature, and R is the ideal gas constant.

Substituting the given values:

Pi * Vi = n * R * Ti

Next, we need to calculate the final volume of the water. As the temperature increases, the volume of the water will change, causing the piston to move. We can calculate the change in volume using the equation:

ΔV = Vf - Vi

Where ΔV is the change in volume, Vf is the final volume, and Vi is the initial volume.

Substituting the given values:

ΔV = Vf - Vi

Finally, we can calculate the work done on the piston using the equation for work done by a gas:

W = P * ΔV

Substituting the calculated values:

W = P * ΔV

Learn more about calculating work done in a cylinder with water and a piston here:

https://brainly.com/question/7383904

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