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In an ideal heat-engine cycle a fixed mass of air is taken through the following four processes - AQA - A-Level Physics - Question 4 - 2019 - Paper 6

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In an ideal heat-engine cycle a fixed mass of air is taken through the following four processes. A → B Isothermal compression from an initial pressure of 1.0 × 10$^... show full transcript

Worked Solution & Example Answer:In an ideal heat-engine cycle a fixed mass of air is taken through the following four processes - AQA - A-Level Physics - Question 4 - 2019 - Paper 6

Step 1

Show, by calculation, that the volume at B is 4.1 × 10$^{-2}$ m$^3$.

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Answer

To find the volume at B, we utilize the ideal gas law, which is given by:

PV=nRTPV = nRT

Since the pressure at A and B is known, we can rearrange the formula to solve for volume:

V=nRTPV = \frac{nRT}{P}

Using the known parameters, we can calculate the volume at point B.

Step 2

Show that the temperature of the air at C is about 420 K.

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Answer

To calculate the temperature at C, we can again use the ideal gas law. We know the pressure at C and can determine the number of moles from the process. The temperature can then be inferred using this relationship. Thus:

TC=PCVCnRT_C = \frac{P_C V_C}{nR}

By substituting in the values for PCP_C, VCV_C, and RR, we can derive the temperature at point C.

Step 3

Complete Table 1 to show the values of work done W and energy transfer Q in each of the four processes.

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Answer

We need to calculate work done and energy transfer for each process as follows:

  • Process A → B:

    • Work done W=−7100extJW = -7100 ext{ J}
    • Energy transfer Q=−7100extJQ = -7100 ext{ J}

  • Process B → C:

    • Work done W=4000extJW = 4000 ext{ J}
    • Energy transfer Q=4000extJQ = 4000 ext{ J}

  • Process C → D:

    • Work done W=10,300extJW = 10,300 ext{ J}
    • Energy transfer Q=10,300extJQ = 10,300 ext{ J}

  • Process D → A:

    • Work done W=−14,000extJW = -14,000 ext{ J}
    • Energy transfer Q=−14,000extJQ = -14,000 ext{ J}

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