Advertisements
Advertisements
Question
A steam engine delivers 5.4×108 J of work per minute and services 3.6 × 109 J of heat per minute from its boiler. What is the efficiency of the engine? How much heat is wasted per minute?
Advertisements
Solution 1
Work done perminute, output =` 5.4 xx 10^8 J`
Heat absorbed per minute, input = `3.6 xx 10^9 J`
Efficiency, = eta = "output"/"input" = (5.4 xx 10^8)/(3.6 xx 10^9) = 0.15
`%eta = 0.15 xx 100 = 15`
Heat energy wasted /minute
= Heat energy absorbed / minute - Useful work done / minute
`= 3.6 xx 10^9 - 5.4 xx 10^8`
`= (3.6 - 0.54) xx 10^9 = 3.06 xx10^9 J`
Solution 2
Work done by the steam engine per minute, W = 5.4 × 108 J
Heat supplied from the boiler, H = 3.6 × 109 J
Efficiency of the engine = `"Output energy"/"Inut energy"`
`:.eta = W/H = (5.4 xx 10^8)/(3.6 xx 10^9) = 0.15`
Hence, the percentage efficiency of the engine is 15 %.
Amount of heat wasted = 3.6 × 109 – 5.4 × 108
= 30.6 × 108 = 3.06 × 109 J
Therefore, the amount of heat wasted per minute is 3.06 × 109 J.
APPEARS IN
RELATED QUESTIONS
Should the internal energy of a system necessarily increase if heat is added to it?
The final volume of a system is equal to the initial volume in a certain process. Is the work done by the system necessarily zero? Is it necessarily nonzero?
An ideal gas is pumped into a rigid container having diathermic walls so that the temperature remains constant. In a certain time interval, the pressure in the container is doubled. Is the internal energy of the contents of the container also doubled in the interval ?
Consider the process on a system shown in figure. During the process, the work done by the system ______________ .
A gas is contained in a metallic cylinder fitted with a piston. The piston is suddenly moved in to compress the gas and is maintained at this position. As time passes the pressure of the gas in the cylinder ______________ .
In a process on a system, the initial pressure and volume are equal to the final pressure and volume.
(a) The initial temperature must be equal to the final temperature.
(b) The initial internal energy must be equal to the final internal energy.
(c) The net heat given to the system in the process must be zero.
(d) The net work done by the system in the process must be zero.
A 100 kg lock is started with a speed of 2.0 m s−1 on a long, rough belt kept fixed in a horizontal position. The coefficient of kinetic friction between the block and the belt is 0.20. (a) Calculate the change in the internal energy of the block-belt system as the block comes to a stop on the belt. (b) Consider the situation from a frame of reference moving at 2.0 m s−1 along the initial velocity of the block. As seen from this frame, the block is gently put on a moving belt and in due time the block starts moving with the belt at 2.0 m s−1. calculate the increase in the kinetic energy of the block as it stops slipping past the belt. (c) Find the work done in this frame by the external force holding the belt.
A gas is taken through a cyclic process ABCA as shown in figure. If 2.4 cal of heat is given in the process, what is the value of J ?
A substance is taken through the process abc as shown in figure. If the internal energy of the substance increases by 5000 J and a heat of 2625 cal is given to the system, calculate the value of J.
A gas is taken along the path AB as shown in figure. If 70 cal of heat is extracted from the gas in the process, calculate the change in the internal energy of the system.
A system releases 100 kJ of heat while 80 kJ of work is done on the system. Calculate the change in internal energy.
Explain the different ways through which the internal energy of the system can be changed.
One gram of water (1 cm3) becomes 1671 cm3 of steam at a pressure of 1 atm. The latent heat of vaporization at this pressure is 2256 J/g. Calculate the external work and the increase in internal energy.
An ideal gas is compressed at a constant temperature. Its internal energy will ____________.
Two samples A and B, of a gas at the same initial temperature and pressure are compressed from volume V to V/2; A isothermally and B adiabatically. The final pressure of A will be ______.
Which of the following represents isothermal process?
Figure shows the P-V diagram of an ideal gas undergoing a change of state from A to B. Four different parts I, II, III and IV as shown in the figure may lead to the same change of state.
- Change in internal energy is same in IV and III cases, but not in I and II.
- Change in internal energy is same in all the four cases.
- Work done is maximum in case I
- Work done is minimum in case II.
The molar specific heat of He at constant volume is 12.47 J/mol.K. Two moles of He are heated at constant pressure. So the rise in temperature is 10 K. Find the increase in internal energy of the gas.
A system releases 125 kJ of heat while 104 kJ work is done on the system. Calculate the change in internal energy.
