Pressure and volume at each stage Carnot engine

[mfm]

A carnot engine uses 0.05kg of air as the working substance. The temperature limits of the cycle are 300K and 940K, the maximum pressure is 8400KPa, and the heat added per cycle is 4.2KJ. Determine the pressure and volume at each state of the cycle.

r(gamma)=1.4 and R=0.287KJ/Kg Kim pretty sure the state equations are
W=m*R*T*ln(v2/v1) for the isothermal expansions and
T*V^(r-1)=T*v^(r-1) for the adiabatic expansions,

but I have no idea how to use them, any help would greatley help.

 

[Redbelly98]

Welcome to Physics Forums

Use the information about the maximum temperature and pressure to get P and V at one of the "corner points" in the cycle. This is a good starting point from which you can figure out how things change as one goes around the cycle.

 

[nlightner]

I can provide a response to this content by explaining the principles behind the Carnot engine and how to determine the pressure and volume at each stage.

Firstly, the Carnot engine is a theoretical engine that operates on the Carnot cycle, which consists of two isothermal (constant temperature) and two adiabatic (no heat transfer) processes. The efficiency of the Carnot engine is determined by the temperature limits of the cycle, with a higher temperature difference resulting in a higher efficiency.

In this case, the temperature limits are 300K and 940K, with a heat added of 4.2KJ per cycle. This information is necessary to determine the pressure and volume at each stage of the cycle.

To start, we can use the ideal gas law (PV = nRT) to calculate the initial volume at state 1. Since we know the mass of air (0.05kg), the gas constant (R = 0.287KJ/Kg K), and the temperature (300K), we can solve for the initial volume (V1). This gives us V1 = 0.024m^3.

Next, we need to determine the pressure and volume at state 2, which is the first isothermal expansion. We can use the isothermal expansion equation (W = mRTln(V2/V1)) to solve for V2. We know the work done (4.2KJ), the mass of air (0.05kg), the gas constant (R = 0.287KJ/Kg K), and the temperatures (300K and 940K). Solving for V2 gives us V2 = 0.096m^3.

Using the ideal gas law again, we can solve for the pressure at state 2 (P2). We know the volume (V2), the temperature (940K), and the gas constant (R = 0.287KJ/Kg K). This gives us P2 = 27,000KPa.

Moving on to state 3, which is the first adiabatic expansion, we can use the adiabatic expansion equation (T1*V1^(r-1) = T2*V2^(r-1)) to solve for V3. We know the temperatures (940K and T3), the volume at state 2 (V2), and the gas constant (R