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The internal energy of a gas is 500J.The gas is compressed adibatically,and its volume dec...

The internal energy of a gas is 500J.The gas is compressed adibatically,and its volume decreases by 100.cm3.If the pressure applied on the gas during compression is 3.00atm,what is the internal energy of the gas after the adiabatic compression?

Step-by-Step Solution

Solution 1
Step #1 of 5

THINK:

An adiabatic process is one in which no heat flows when the state of a system changes. Hence, for adiabatic process the heat acquired by the system is.

Step #2 of 5

RESEARCH:

When the process is adiabatic, from the thermo dynamic first law the change in internal energy is given by the equation

Here is the heat acquired by the system and is the work done by the system.

Step #3 of 5

SIMPLIFY:

Let andare the initial and final internal energies then the above equation become as

...... (1)

Let be the pressure and volume change then the work done is

...... (2)

Using equations (1) and (2), the final internal energy of the gas in this adiabatic compression process is

...... (3)

Step #4 of 5

Given data:

The initial internal energy of the gas,

The decreased volume of the gas,

The pressure of the gas,

Step #5 of 5

CALCULATE:

Now, substituting the numerical values in equation (3), we get

Therefore, the internal energy of the gas after the adiabatic compression is.

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