Suppose 2.40 mol of an ideal gas of volume V1 = 4.00 m3 at T1 = 290 K is allowed to expand isothermally to V2 = 24.0 m3 at T2 = 290 K .
Part A
Determine the work done by the gas.
|
||||
W= |
(a)
Work done ON the gas is given by the integral:
W = - ∫ p dV from V₁ to V₂
We have a constant temperature process on an ideal gas, that
means
p∙V = n∙R∙T = constant throughout the whole process.
Hence:
p∙V = p₁∙V₁
<=>
p = p₁∙V₁/V
Substitute this expression to the work integral:
W = - ∫ p₁∙V₁/V dV from V₁ to V₂
= - p₁∙V₁∙ ∫ 1/V dV from V₁ to V₂
= - p₁∙V₁ ∙ ln( V₂/V₁ )
since p₁∙V₁ = n∙R∙T₁
W = - n∙R∙T₁ ∙ ln( V₂/V₁ )
= - 2.40mol ∙ 8.3145J/molK ∙ 290K ∙ ln(24.0m³ / 4m³ )
= -10368.71J
So 10368.71 Joules of work are done BY the gas.
Suppose 2.00 mol of an ideal gas of volume V =3.50m^3 at T = 300K .allowed to expand isothermally to V = 7.00m^3 at T = 300K. Determine (a) the work done by heat added to the gas. and (c) the change in internal energy of the gas. (Ans: 3.6 times 10^3, J, 0, 3.6 times 10^3J)
An ideal gas is allowed to expand isothermally until it reaches its final volume. It is then heated at constant volume until it reaches its final pressure. The initial state of the gas is P1 = 2.93 atm, V1 = 1.00 L, and Eint 1 = 414 J, and its final state has volume V2 = 2.93 L and Eint 2 = 951 J. 1) Calculate the work done by the gas. Be careful with signs: if the work you...
2 moles of compressed air (diatomic gas) in a cylinder under the initial condition T1=573K p1=500kPa. Found v1=0.019m^3 but can not remember then how to find V2. I think that it has something to do with T1=T2 condition then P2 can be found.... but stuck on how to proceed so with FULL written explanations with working would be much appreciated! All question info on practice exam below - note ISOTHERMAL EXPANSION. for part ii which after an explanation first. Two...
In an industrial process the volume of 25.0 mol of a monatomic ideal gas is reduced at a uniform rate from 0.616 m3 to 0.308 m3 in 2.00 h while its temperature is increased at a uniform rate from 27.0°C to 450°C. Throughout the process, the gas passes through thermodynamic equilibrium states. What are (a) the cumulative work done by the gas, (b) the cumulative energy absorbed by the gas as heat, and (c) the molar specific heat for the...
Isobaric processes V1 = 5 m3 P1 = 200 kPa T1 = 273 K What is V2 and T2? I do not have a value for either V2 or T2.
Suppose 1.5 mol of an ideal gas is taken from a volume of 3.2 m3 to a volume of 1.6 m3 via an isothermal compression at 25°C. (a) How much energy is transferred as heat during the compression, and (b) is the transfer to or from the gas?
A cylinder of volume 0.290 m3 contains 10.6 mol of neon gas at 20.6°C. Assume neon behaves as an ideal gas. (a) What is the pressure of the gas? Pa (b) Find the internal energy of the gas. J (c) Suppose the gas expands at constant pressure to a volume of 1.000 m3. How much work is done on the gas? J (d) What is the temperature of the gas at the new volume? K (e) Find the internal energy...
A volume of 100 m3 of a non-ideal gas is contained at 150°C and 50 bar. The gas is then compressed isothermally to a pressure of 300 bar in a well-designed compressor. What is the volume of the compressed gas, how much work is done to compress it, and how much heat must be removed to maintain the temperature at 150°C during compression? You may apply the principle of corresponding states. The critical properties of the non-ideal gas are Tc...
A 1.00-mol sample of an ideal diatomic gas is allowed to expand. This expansion is represented by the straight line from 1 to 2 in the PV diagram. The gas is then compressed isothermally. This compression is represented by the curved line from 2 to 1 in the PV diagram. Calculate the work per cycle done by the gas.
With the pressure held constant at 230 kPa, 44 mol of a
monatomic ideal gas expands from an initial volume of 0.80 m3 to a
final volume of 1.9 m3.
Review PartA With the pressure held constant at 230 kPa, 44 mol of a monatomic ideal gas expands from an initial volume of 0.80 m3 to a final volume of 1.9 m3 How much work was done by the gas during the expansion? Express your answer using two significant figures....