Energy into a rigid container>Find T2 and P2

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In summary, the problem involves a fan drawing electricity at a rate of 1.5kW in a well-insulated rigid container of air with an initial volume and pressure of 60 m^3 and 1 atm, respectively. After 30 minutes, assuming ideal gas behavior, the final temperature and pressure need to be determined. The equations used include ΔE = Q - W, PV = nRT, and ΔU = mc(T2-T1). The calculated energy into the system after 30 minutes is 2700.8 kJ and since there is no change in kinetic or potential energy, ΔE = ΔU. With no heat transfer (Q = 0), the work done on the system is -270
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Homework Statement


A Fan draws electricity at a rate of 1.5kW.
The fan is in a well insulated rigid container of air with volume 60 m^3.
Initial pressure and Initial Volume are: P1 = 1 atm, T1 = 27 degrees C.
After 30 minutes, assume Ideal Gas behavior, determine the final Temp and final Pressure.

Homework Equations



ΔE = Q - W
PV=nRT
ΔU=mc(T2-T1)?

The Attempt at a Solution



I calculated the energy into the system to be 2700.8 kJ after 30 minutes. Since there is no ΔKE or ΔPE, ΔE = ΔU = 2700.8 kJ. Since it is well insulated, Q = 0. So W = -2700.8 kJ.

I am having trouble linking the relationship between Energy and Temperature/Volume. I am not sure what other equations to use, so I am making no progress on this problem.
 
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Does anyone have some advice. I will take anything that points me in the right direction, lol.
 

Related to Energy into a rigid container>Find T2 and P2

1. What is Energy into a rigid container?

Energy into a rigid container refers to the process of transferring energy into a container that is unable to expand or deform. This means that the volume, shape, and size of the container remains constant during the energy transfer.

2. Why is it important to find T2 and P2 in this process?

T2 and P2 represent the final temperature and pressure of the system after the energy transfer. It is important to find these values in order to understand how the energy has affected the system and to ensure that the container can withstand the resulting temperature and pressure changes.

3. How do you calculate T2 and P2?

T2 and P2 can be calculated using the ideal gas law, which states that the pressure and volume of a gas are directly proportional to its temperature and number of moles. The equation used to calculate T2 and P2 is: P1V1/T1 = P2V2/T2, where P1 and T1 represent the initial pressure and temperature, and V2 and T2 represent the final volume and temperature.

4. What factors can affect the values of T2 and P2?

The values of T2 and P2 can be affected by a variety of factors, including the amount of energy transferred, the type of gas in the container, and the initial temperature and pressure of the system. The type of container and any external influences, such as heat transfer or work done, can also impact T2 and P2.

5. Why is a rigid container used in this process?

A rigid container is used in this process to ensure that the volume of the container remains constant and that the energy transfer does not result in any changes to the container's shape or size. This allows for more accurate calculations of T2 and P2 and helps to maintain the integrity of the system.

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