Advertisements
Advertisements
प्रश्न
Can two states of an ideal gas be connected by an isothermal process as well as an adiabatic process?
उत्तर
For two states to be connected by an isothermal process,
P1V1 = P2V2 ... (i)
For the same two states to be connected by an adiabatic process,
P1V1γ = P2V2γ ...(ii)
If both the equations hold simultaneously then, on dividing eqaution (ii) by (i) we get
V1γ-1 = V2γ-1
Let the gas be monatomic. Then,
γ =`5/3`
`=> "V"_1^ (2/3)= "V"_2^(2/3)`
⇒ V1 = V2
If this condition is met, then the two states can be connected by an isothermal as well as an adiabatic process.
APPEARS IN
संबंधित प्रश्न
A metre long narrow bore held horizontally (and closed at one end) contains a 76 cm long mercury thread, which traps a 15 cm column of air. What happens if the tube is held vertically with the open end at the bottom?
Does a gas have just two specific heat capacities or more than two? Is the number of specific heat capacities of a gas countable?
Does a solid also have two kinds of molar heat capacities Cp and Cv? If yes, is Cp > Cv? Or is Cp − Cv = R?
In a real gas, the internal energy depends on temperature and also on volume. The energy increases when the gas expands isothermally. Examining the derivation of Cp − Cv = R, find whether Cp − Cv will be more than R, less than R or equal to R for a real gas.
Show that the slope of the p−V diagram is greater for an adiabatic process compared to an isothermal process.
In an isothermal process on an ideal gas, the pressure increases by 0.5%. The volume decreases by about
Let ∆Wa and ∆Wb be the work done by the systems A and B, respectively, in the previous question.
5 g of a gas is contained in a rigid container and is heated from 15°C to 25°C. Specific heat capacity of the gas at constant volume is 0.172 cal g−1 °C−1 and the mechanical equivalent of heat is 4.2 J cal−1. Calculate the change in the internal energy of the gas
An ideal gas expands from 100 cm3 to 200 cm3 at a constant pressure of 2.0 × 105 Pa when 50 J of heat is supplied to it. Calculate (a) the change in internal energy of the gas (b) the number of moles in the gas if the initial temperature is 300 K (c) the molar heat capacity Cp at constant pressure and (d) the molar heat capacity Cv at constant volume.
The speed of sound in hydrogen at 0°C is 1280 m s−1. The density of hydrogen at STP is 0.089 kg m−3. Calculate the molar heat capacities Cp and Cv of hydrogen.
4.0 g of helium occupies 22400 cm3 at STP. The specific heat capacity of helium at constant pressure is 5.0 cal K−1 mol−1. Calculate the speed of sound in helium at STP.
Standing waves of frequency 5.0 kHz are produced in a tube filled with oxygen at 300 K. The separation between the consecutive nodes is 3.3 cm. Calculate the specific heat capacities Cp and Cv of the gas.
Molar specific heat of water is C = 74.7 J/mol K, its value in cal/g K is ______.
An engine takes in 5 moles of air at 20°C and 1 atm, and compresses it adiabatically to `1/10^"th"` of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be X kJ. The value of X to the nearest integer is ______.
