A cylinder contains 3.0 L of oxygen at 310 K and 2.5 atm. The gas is heated, causing a piston in the cylinder to move outward. The heating causes the temperature to rise to 610 K and the volume of the cylinder to increase to 9.5 L. What is the gas pressure? P= _____atm

Respuesta :

Answer:

The gas pressure is: 1.55 atm.

Explanation:

We need to use the equation that relate the variables given at the exercise (pressure, temperature and volume) from the ideal gas law formula, when the mass is constant we can reduce the expretion [tex]PV=nRT[/tex] to [tex]\frac{P_{1}V_{1}}{T_{1}}=\frac{P_{2}V_{2}}{T_{2} }[/tex] solving to P2 we get:[tex]\frac{P_{1}V_{1}T_{2}}{T_{1}V_{2}}=P_{2}[/tex] replace the values [tex]P_{2}=\frac{2.5*3*610}{9.5*310} =1.55(atm)[/tex].

For a closed system, the amount of oxygen remains the same inside the cylinder. Then the pressure after heating is 1.6 atm.

What is thermodynamics?

It is a branch of science that deals with heat and work transfer.

We know that the ideal gas equation is given as

PV = nRT

P = Pressure

V = Volume

n = number of mole

R = Universal gas constant

T = Temperature (in K)

A cylinder contains 3.0 L of oxygen at 310 K and 2.5 atm.

The gas is heated, causing a piston in the cylinder to move outward.

The heating causes the temperature to rise to 610 K and the volume of the cylinder to increase to 9.5 L.

For a closed system, the amount of oxygen remains the same inside the cylinder.

[tex]\dfrac{PV}{T} = C[/tex]

Then we have

[tex]\rm \dfrac{P_2V_2}{T_2} =\dfrac{P_1V_1}{T_1} \\\\\\ \dfrac{P_2*9.5}{610} =\dfrac{2.5*3}{310}\\\\\\P_2 = 1.553 \approx 1.6[/tex]

More about the thermodynamics link is given below.

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