Does the temperature of an ideal gas increase, decrease, or stay the same during (a) an isothermal expansion, (b) an expansion at constant pressure, (c) an adiabatic expansion, and (d) an increase in pressure at constant volume?
The gas is an ideal gas.
Since the temperature remains constant in an isothermal process, the temperature of an ideal gas during an isothermal expansion stays the same. Using the gas law, we can predict the temperature of an ideal gas during an expansion at constant pressure and during an increase in pressure at constant volume. Then, using the first law of thermodynamics, we can predict the temperature of an ideal gas during an adiabatic expansion.
Ideal gas equation, …(i)
Change in internal energy due to first law of thermodynamics, …(ii)
Change in internal energy at constant volume, …(iii)
For an ideal gas at isothermal expansion, the initial temperature and final temperature is the same, so
Hence, the temperature of an ideal gas during an isothermal expansion stays the same.
For constant pressure, there is change in volume. Thus, the equation (i) gives the temperature value as follows:
Since, thus, the value of change in temperature using the above equation is
Hence, the change in temperature increases at constant pressure.
For adiabatic expansion, the total heat is constant, i.e.
Thus, using equation (ii), the change in internal energy is given as follows:
For adiabatic expansion, gas is expanding, so that work done is positive and is increasing.
Now, using this value in equation (iii), we can get the change in temperature as follows:
Hence, the change in temperature decreases at constant adiabatic expansion.
For constant volume, there is change in pressure. Thus, equation (i) gives the temperature value as follows:
Since, the change in internal energy is found using the above equation as
Therefore, the change in temperature increases with an increase in the pressure at constant volume.
Figure shows a cycle undergone by 1.00mol of an ideal monoatomic gas. The temperatures are T1=300K, T2=600K and T3=455K. For , what are- (a) Heat Q (b) The change in internal energy (c) The work done W? For, (d) What is Q? (e) What is Q? (f) What is W? For , (g) What is Q? (h) What is ? (i) What is W? For the full cycle, (j) What is Q? (k)What is ? (l) What is W? The initial pressure at point 1 is 1.00atm. What are the (m) volume and (n) pressure at point 2? What are the (o) volume and (p) pressure at point 3?
Question: A container encloses 2 mol of an ideal gas that has molar mass M1 and 0.5 mol of a second ideal gas that has molar mass m2 = 3 .m1 What fraction of the total pressure on the container wall is attributable to the second gas? (The kinetic theory explanation of pressure leads to the experimentally discovered law of partial pressures for a mixture of gases that do not react chemically: The total pressure exerted by the mixture is equal to the sum of the pressures that the several gases would exert separately if each were to occupy the vessel alone.)
Figure shows two paths that may be taken by a gas from an initial point i to a final point f. Path 1 consists of an isothermal expansion (work is in magnitude), an adiabatic expansion (work is in magnitude), an isothermal compression (work is 30J in magnitude) and then an adiabatic compression (work is 25J in magnitude). What is the change in the internal energy of the gas if the gas goes from point i to point f along path 2?
An ideal gas with is initially in state 1 with pressure and volume . First it is taken to state 2 with pressure and volume . Then it is taken to state 3 with pressure and volume . What is the temperature of the gas in
(a) state 1 and
(b) state 2?
(c) What is the net change in internal energy from state 1 to state ?
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