The efficiency of a heat engine is given by the expression 
The efficiency of a heat engine is the ratio of the work done by the engine to the heat given as the input to the engine.

The heat engine absorbs Q h from the hot reservoir , performs a work <em>W</em> on the absorbed heat and rejects Qc to the cold reservoir.
Therefore, the work done is given by,

Thus the efficiency is given by, 
Answer:
is proved.
Explanation:
The magnetic field in the long current carrying wire is,

Here, I is the current, B is the magnetic field.
Now, by using cylindrical coordinates for the divergence of B.

Put the value of B in above equation.

Hence, it is prove that for a long current I carrying wire magnetic field divergence that is
.
Answer:
f = 735 Hz
Explanation:
given,
Person distance from speakers
r₁ = 4.1 m r₂ = 4.8 m
Path difference
d = r₂ - r₁ = 4.8 - 4.1 = 0.7 m
For destructive interference

where, n = 1, 3,5..
we know, λ = v/f

v is the speed of the sound = 343 m/s
f is the frequency

for n = 1

f = 245 Hz
for n = 3

f = 735 Hz
Hence,the second lowest frequency of the destructive interference is 735 Hz.
Answer:
<em>a. The rock takes 2.02 seconds to hit the ground</em>
<em>b. The rock lands at 20,2 m from the base of the cliff</em>
Explanation:
Horizontal motion occurs when an object is thrown horizontally with an initial speed v from a height h above the ground. When it happens, the object moves through a curved path determined by gravity until it hits the ground.
The time taken by the object to hit the ground is calculated by:

The range is defined as the maximum horizontal distance traveled by the object and it can be calculated as follows:

The man is standing on the edge of the h=20 m cliff and throws a rock with a horizontal speed of v=10 m/s.
a,
The time taken by the rock to reach the ground is:


t = 2.02 s
The rock takes 2.02 seconds to hit the ground
b.
The range is calculated now:

d = 20.2 m
The rock lands at 20,2 m from the base of the cliff
Answer:
by applying a magnetic force to recycled materials