The change in internal energy of the gas is

.
In fact, the 1st law of thermodynamics states that the change in internal energy of a system is equal to the amount of heat given to the system (Q) plus the work done on the system (W):

In this example, no work is done on the bottle so W=0, while the heat given to the system is

, so the change in internal energy of the gas is
Answer:
1196.02 °C
Explanation:
If the kinetic energy is converted into heat,
then,
Kinetic energy of the copper = heat energy of the copper
1/2m(v²) = cm(t₂-t₁)
where m = mass of copper, v = velocity of copper, c = specific heat capacity of copper, t₂ = final temperature of copper, t₁ = initial temperature of copper.
Since the mass of copper remains the same,
1/2v² = c(t₂-t₁)
make t₂ the subject of the equation
t₂ = 1/2(v²/c)+t₁..................... Equation 1
Given: v = 950 m/s, c = 387 J/kg°C, t₁ 30 °C
Substitute into equation 1
t₂ = 1/2(950²/387)+30
t₂ = 1196.02 °C
Hence the temperature the bullet reach before it was stopped = 1196.02 °C
Answer:

Explanation:
From the question we are told that:
Mass of pulley 
Radius 
Mass of block A 
Mass of block B 
Spring constant
Generally the equation for Torque is mathematically given by
Since 
At mass A

At mass B

At Pulley


Therefore the equation for total force F
At mass A+At mass B+At Pulley




Since From above equation

Therefore



Generally the equation for frequency is mathematically given by


Answer:
Force must be applied to m₁ to move the group of rocks from the road at 0.250 m/s² = 436 N
Explanation:
Total force required = Mass x Acceleration,
F = ma
Here we need to consider the system as combine, total mass need to be considered.
Total mass, a = m₁+m₂+m₃ = 584 + 838 + 322 = 1744 kg
We need to accelerate the group of rocks from the road at 0.250 m/s²
That is acceleration, a = 0.250 m/s²
Force required, F = ma = 1744 x 0.25 = 436 N
Force must be applied to m₁ to move the group of rocks from the road at 0.250 m/s² = 436 N
Answer:
(a). 12 plants
(b). 3171 $
Explanation:
(a)first convert units of 100 billion kWh/year into Watts(W)
also convert the units of 1000 MW into Watts(W)
1 billion = 10^9
1 year = 365*24 = 8760 hrs
so
100 billion kWh/year = 1
=
W
1000 MW = 
no. of plants =
= 11.4
So 12 plants required
(b)
savings = unit price*total units
= 
= 3170.9 =3171 $