Find the electrical energy supplied in kJ and kWhr

[udontai]

Homework Statement

a mass of 15kg of air in piston-cylinder assembly is heated from 25°C to 77°C by passing current through a resistance heater inside the cylinder. the pressure inside the cylinder held constant at 300kPa during the process and heat loss of 60kJ occurs. (Cv= 0.718 kJ/kgK)

i) find the electrical energy supplied in kJ and kWhr

Homework Equations

The Attempt at a Solution

W-60k = 15 (0.718)(52)
W= 620.04kJ
so to find the energy in kWhr, take 620.04 /3600? is it correct?

 

[Chestermiller]

Yes.

 

[udontai]

For the internal energy. I should apply cp or cv? The pressure is constant

 

[Chestermiller]

For the internal energy. I should apply cp or cv? The pressure is constant

Most conveniently, you could use Cp to get the enthalpy change (which is equal to the heat added at constant pressure). You can also work with Cv to get the change in internal energy, but in this case, you would need to include the PΔV=nRΔT to calculate the heat load. Either way, you get the same answer. Do you know the relationship between Cp and Cv for an ideal gas? If so, use it.

Chet

 

[HalfLostAndSearching]

I would approach this problem by first identifying the relevant equations and units. The given information includes the mass of air, temperature change, pressure, specific heat, and heat loss. The relevant equation for calculating electrical energy is W=Q+U, where W is the electrical energy, Q is the heat added to the system, and U is the internal energy of the system. The units for electrical energy are typically in joules (J) or kilojoules (kJ).

To find the electrical energy supplied in kJ, we can use the given information and the equation W=Q+U. We know that Q=m*Cv*ΔT, where m is the mass of the air, Cv is the specific heat, and ΔT is the temperature change. Plugging in the values, we get Q=15*0.718*(77-25)=620.04 kJ. We also know that U=0, since the pressure is held constant and there is no work done. Therefore, W=620.04 kJ.

To convert this to kWhr, we need to divide by the conversion factor 3600 seconds/hour. This gives us 620.04 kJ/3600 s=0.17223 kWhr. So the electrical energy supplied in kWhr is approximately 0.172 kWhr.

In conclusion, the electrical energy supplied in kJ is 620.04 kJ and in kWhr is 0.172 kWhr. It is important to note that this calculation assumes all of the electrical energy is converted to heat and there are no other energy losses or conversions in the system.