Internal Energy: gas inside piston

[cokeaddict]

A cylinder (cross section is 0.2m2) with a free moving piston is filled with gas. The piston is attached to a heavy weight W = 10000N. Outside the cylinder, the air is at 300K and 1atm. Initially the gas is at 300K, then it is heated to 400K. The heat capacity of the gas under the constant pressure is 500J/K.

If the length of the gas in the cylinder l increases by 20cm during the heating, find the change in the internal energy of the gas in Joule J.


Im thinking:

C = Q / delta T

C (delta T) = Q

500 x (400-300) = 50000 J = Q

so...delta U = Q - W

W = P delta V

i guess P is the pressure inside the piston...I've told something like this:

Inside pressure = outside pressure - weight_force/cross_sectional_area

I tried that, i came up with 456500 = ( 101300 - 10000) / .2

? i don't know...any help would be appreciated...

 

[cokeaddict]

oops, i actually got it...thanks though...

 

[Architeuthis Dux]

I would like to clarify some of the concepts and equations used in this scenario.

Firstly, internal energy refers to the total energy of a system, including the kinetic and potential energy of its particles. In this case, the internal energy of the gas inside the piston will change as it is heated, leading to an increase in temperature and possibly a change in volume.

The heat capacity of the gas refers to the amount of heat required to raise the temperature of the gas by 1 Kelvin. In this case, the heat capacity is given as 500 J/K, meaning that 500 Joules of heat is required to raise the temperature of the gas by 1 Kelvin.

The equation C = Q/delta T is known as the specific heat capacity equation, where C represents the heat capacity, Q represents the heat added, and delta T represents the change in temperature. This equation can only be used for substances with constant heat capacity, which may not be the case for this gas.

In order to calculate the change in internal energy (delta U), we need to use the first law of thermodynamics, which states that the change in internal energy (delta U) is equal to the heat added (Q) minus the work done (W) by the system. In this case, the work done is the pressure (P) times the change in volume (delta V).

To determine the pressure inside the piston, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature. We can rearrange this equation to solve for P, and then use it to calculate the work done by the gas.

Once we have all the necessary values, we can plug them into the first law of thermodynamics equation to calculate the change in internal energy (delta U). This will give us the change in internal energy in Joules, which is the desired answer.

In summary, to find the change in internal energy of the gas inside the piston, we need to use the first law of thermodynamics, the ideal gas law, and the specific heat capacity equation to calculate the heat added, work done, and ultimately the change in internal energy.