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:

Explanation:
Given:
Initial mass of isotope (m₀) = 20 g
Half life of the isotope
= (ln 4) years
The general form for the radioactive decay of a radioactive isotope is given as:

Where,

So, the equation is: 
At half-life, the mass is reduced to half of the initial value.
So, at
. Plug in these values and solve for 'k'. This gives,

Hence, the equation for the mass remaining is given as:

The initial kinetic energy of the cart is

(1)
where m is the mass of the cart and v its initial velocity.
Then, the cart hits the spring compressing it. The maximum compression occurs when the cart stops, and at that point the kinetic energy of the cart is zero, so all its initial kinetic energy has been converted into elastic potential energy of the spring:

where k is the spring constant and x is the spring compression.
For energy conservation, K=U. We can calculate U first: the compression of the spring is x=60 cm=0.60 m, while the spring constant is k=250 N/m, so

So, the initial kinetic energy of the cart is also 45 J, and from (1) we can find the value of the initial velocity:
Answer: Given: h₀=5cm
p=30cm
hi
f=45cm
require: q=?
hi=?
formulas:
1/f=1/p+1/q
hi/h₀=q/p
calculations:1/q=1/f-1/p
1/q=1/45-1/30
1/q=0.022=0.033
1/q= = -0.011
q=1/-0.011
q= -90.91cm
hi=p × h₀/q
hi=30ₓ5/-90.91
hi=150/-90.91
hi= -1.65cm
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