Advertisements
Advertisements
प्रश्न
A gas is enclosed in a cylindrical vessel fitted with a frictionless piston. The gas is slowly heated for some time. During the process, 10 J of heat is supplied and the piston is found to move out 10 cm. Find the increase in the internal energy of the gas. The area of cross section of the cylinder = 4 cm2 and the atmospheric pressure = 100 kPa.
उत्तर
Given:- Heat supplied to the system, ∆Q = 10 J
Change in volume of the system, ∆V = Area of cross section × Displacement of the piston
= A × 10 cm
= (4 × 10) cm3 = 40 × 10−6 m3
P = 100 kPa
∆W = P∆V = 100 × 103 × 40 × 10−6 m3
= 4 J
∆U = ?
Using the first law of thermodynamics, we get
10 = ∆U + ∆W
⇒ 10 = ∆U + 4
⇒ ∆U = 6 J
Here, positive sign indicates that the internal energy of the system has increased.
APPEARS IN
संबंधित प्रश्न
An electric heater supplies heat to a system at a rate of 100W. If the system performs work at a rate of 75 Joules per second. At what rate is the internal energy increasing?
50 cal of heat should be supplied to take a system from the state A to the state B through the path ACB as shown in figure. Find the quantity of heat to be suppled to take it from A to B via ADB.
A solar cooker and a pressure cooker both are used to cook food. Treating them as thermodynamic systems, discuss the similarities and differences between them.
A mixture of hydrogen and oxygen is enclosed in a rigid insulating cylinder. It is ignited by a spark. The temperature and pressure both increase considerably. Assume that the energy supplied by the spark is negligible, what conclusions may be drawn by application of the first law of thermodynamics?
A sample of gas absorbs 4000 kJ of heat and surrounding does 2000 J of work on sample. What is the value of ∆U?
In a given process for an ideal gas, dW = 0 and dQ < 0. Then for the gas ____________.
Consider a cycle tyre being filled with air by a pump. Let V be the volume of the tyre (fixed) and at each stroke of the pump ∆V(V) of air is transferred to the tube adiabatically. What is the work done when the pressure in the tube is increased from P1 to P2?
Consider one mole of perfect gas in a cylinder of unit cross section with a piston attached (figure). A spring (spring constant k) is attached (unstretched length L) to the piston and to the bottom of the cylinder. Initially the spring is unstretched and the gas is in equilibrium. A certain amount of heat Q is supplied to the gas causing an increase of volume from V0 to V1.
- What is the initial pressure of the system?
- What is the final pressure of the system?
- Using the first law of thermodynamics, write down a relation between Q, Pa, V, Vo and k.
Write the mathematical equation for the first law of thermodynamics for:
Adiabatic process
In the reported figure, heat energy absorbed by a system in going through a cyclic process is ______ πJ.
Which among the following equations represents the first law of thermodynamics under isobaric conditions?
If one mole of monoatomic gas `(gamma=5/3)` is mixed with one mole of diatomic gas `(gamma=7/5)`, the value of γ for the mixture is ______.
What work will be done, when 3 moles of an ideal gas are compressed to half the initial volume at a constant temperature of 300 K?
An ideal gas (γ = 1.5) is expanded adiabatically. How many times has the gas had to be expanded to reduce the root mean square velocity of molecules two times?
If the adiabatic ratio for a gas is 5/3, find the molar specific heat capacity of the gas at (i) constant volume (ii) constant pressure.
In an adiabatic process, W = ______.
Explain the formulation of first law of thrmodynamics.
A monoatomic gas at 27°C is adiabatically compressed to 80% of its initial volume. Find the final temperature of the gas.
