Question

In: Chemistry

Consider a container with a frictionless piston that contains a given amount of an ideal gas....

Consider a container with a frictionless piston that contains a given amount of an ideal gas. Assume the initial volume of the gas is 7 L, the initial temperature of the gas is 22.1 °C, and the system is in equilibrium with an external pressure of 1.1 bar. In step 1, the gas is cooled reversibly to a final temperature -29.9 °C. The external pressure remains constant at all times. In step 2 the gas is heated at constant volume to a final temperature 4.1 °C.

A) What is the final pressure of the gas?

B) What is the final volume?

C) Calculate w for the overall process (steps 1 + 2)

Solutions

Expert Solution

A)

In step 2 the gas is heated at constant volume to a final temperature 4.1 °C.

V2 = V3 = 5.767 L

So,T3 = 4.1 °C =277.1K

T2 =-29.9 °C. = 243.1K

Pressure   P2= 1.1 bar.

Final pressure of the gas P3 = ?

P2V2/T2 = P3V3/T3

P3 = P2V2T3/ V3T2

P2 = (1.1 x 5.767 x 277.1)/(5.767 x 243.1) = 1.25 bar

Final pressure of the gas is 1.25 bar

B)

Initial volume of the gas V1 = 7 L

The initial temperature of the gasT1 = 22.1 °C = 295.1K

The final temperature T2 -29.9 °C =243.1K

Now calculate the final volume V2 by using equation

P1V1/T1 = P2V2/T2

V2 = P1V1T2 /P2T1

(1.1bar x7L x 243.1K)/(1.1bar x 295.1K) = 5.767 L

Final volume = 5.767L

C) Calculate w for the overall process (steps 1 + 2)

W for the steps 1 =

W1 = P ( V2 - V1)

      = 1.1 (5.767- 7.0 ) = - 1.356 KJ

W2 for the steps 2 = 0

Because the volume is constant in step 2, soW2 = 0

w for the overall process (steps 1 + 2) = - 1.36 KJ+ 0 = - 1.36 KJ

queen_honey_blossom answered 2 years ago
Next > < Previous

Related Solutions

Consider a container with a frictionless piston that contains a given amount of an ideal gas....
Consider a container with a frictionless piston that contains a given amount of an ideal gas. Let’s assume that initially the external pressure is 2.20 bar, which is the sum of a 1 bar atmospheric pressure and the pressure created by a very large number of very small pebbles that rest on top of the piston. The initial volume of gas is   0.300 L   and the initial temperature is 25°C. Now, you will increase the volume of the gas by...
a) Consider an ideal gas in a container with a frictionless piston. The gas is isothermally...
a) Consider an ideal gas in a container with a frictionless piston. The gas is isothermally compressed at 26 degrees Celsius as 940 Joules of work is done on it. Determine the resulting change in entropy of the gas, the change in entropy of the environment and the universe. (assume the temperature of the environment is a constant 22 Celsius) b) 20 grams of ice at 0 Celsius melt while being left at room temperature of 22 Celsius. After melting,...
Consider 10 moles of an ideal polyatomic gas in a container with a frictionless piston. The...
Consider 10 moles of an ideal polyatomic gas in a container with a frictionless piston. The initial pressure is 105 kPascals and initial volume is .3 m3.   The gas is isobarically compressed to .1 m3. Determine the resulting change in entropy of the environment. (assume the temperature of the environment is a constant 28 Celsius) Group of answer choices a) +453.6 J/K b) +426.4 J/K c) +313.8 J/K d) +349.2 J/K e) +376.4 J/K
Challenge: pV work 2 Consider a container with a frictionless piston that contains a given amount...
Challenge: pV work 2 Consider a container with a frictionless piston that contains a given amount of CO2. Assume that the behavior of this gas can be described by the van der Waals equation of state. For carbon dioxide gas (CO2), the constants in the van der Waals equation are a=0.364J⋅m3/mol2 and b=4.27×10−5m3/mol. Let’s assume that initially the external pressure is 2.20 bar, which is the sum of a 1 bar atmospheric pressure and the pressure created by a very...
Constant amount of ideal gas is kept inside a cylinder by a piston. The piston is...
Constant amount of ideal gas is kept inside a cylinder by a piston. The piston is locked in to position, it is not allowed to move. The gas is then heated up. Compare the initial (i) and the final (f) physical quantities of the gas to each other. (The fill in the blank options are greater than, less than, or equal too). The volume Vf is ... Vi. The temperature Tf is ... Ti. The internal energy Uf is ......
A horizontal rectangular piston contains 1.85 mol of a polyatomic ideal gas at a pressure of...
A horizontal rectangular piston contains 1.85 mol of a polyatomic ideal gas at a pressure of 1.013x10^5 Pa and a temperature of 322.5 C. The gas within the piston is cooled to 264.0 C. (a) If the piston undergoes an isovolumetric process, what is the change in entropy of the gas? J/K (b) If the piston undergoes an isobaric process inside the chamber, what is the change in entropy of the gas? J/K
A piston contains 620 moles of an ideal monatomic gas that initally has a pressure of...
A piston contains 620 moles of an ideal monatomic gas that initally has a pressure of 2.92 × 105 Pa and a volume of 4.1 m3. The piston is connected to a hot and cold reservoir and the gas goes through the following quasi-static cycle accepting energy from the hot reservoir and exhausting energy into the cold reservoir. The pressure of the gas is increased to 5.92 × 105 Pa while maintaining a constant volume. The volume of the gas...
An engine that operates by means of an ideal diatomic ideal gas in a piston with...
An engine that operates by means of an ideal diatomic ideal gas in a piston with 2.70 moles of gas. The gas starts at point A with 3x103 Pa of pressure and 2.5x10-2 m3. To get from B from A, it is expanded by an isobaric process to double the initial volume. From B to C it expands adiabatically until it reaches three times the volume in A. From C to D the pressure decreases without changing the volume and...
Please include detailed work for answers A piston contains 770 moles of an ideal monatomic gas...
Please include detailed work for answers A piston contains 770 moles of an ideal monatomic gas that initally has a pressure of 1.23 × 105 Pa and a volume of 4.2 m3. The piston is connected to a hot and cold reservoir and the gas goes through the following quasi-static cycle accepting energy from the hot reservoir and exhausting energy into the cold reservoir. The pressure of the gas is increased to 4.23 × 105 Pa while maintaining a constant...
A cylinder containing ideal gas is sealed by a piston that is above the gas. The...
A cylinder containing ideal gas is sealed by a piston that is above the gas. The piston is a cylindrical object, with a weight of 36.0 N, which can slide up or down in the cylinder without friction. The inner radius of the cylinder, and the radius of the piston, is 7.00 cm. The top of the piston is exposed to the atmosphere, and the atmospheric pressure is 101.3 kPa. The cylinder has a height of 30.0 cm, and, when...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT