Al Azhar university Lama El Banna general physic

1. General Physics for Medical Sciences
Homework 4 Solution
Instructor: Dr. Hassan Ashour
1. The temperature difference between the inside and the outside of an automobile engine is 450°C.
Express this temperature difference on the (a) Fahrenheit scale and (b) Kelvin scale.
Solution:
∆℉ =
9
5
∆℃ → ∆℉ =
9
5
× 450 = 810 ℉
∆ = ∆℃ = 450
2. An ideal gas with volume of 3 Litres is compressed at fixed temperature by increasing its
pressure to 250 kPa. Find the bulk modulus of this gas.
Solution:
Compressed at fixed temperatures mean = .
= →
−
=
−
−∆
=
∆
→ ∆ = −
∆
(1)
= −
∆
∆ /
→ ∆ = −
∆
1
(2)
Comparing equations 1 and 2, you will find = = 250
3. A steel rod 4.00 cm in diameter is heated so that its temperature increases by 70.0°C. It is then
fastened between two rigid supports. The rod is allowed to cool to its original temperature.
Assuming that Young’s modulus for the steel is 20.6 × 10 / and that its average coefficient
of linear expansion is 11 × 10 ℃ , calculate the tension in the rod.
Solution:
∆ = ∆ =
=
∆
= ×
∆
= ∆ = 20.6 × 10 × (2 × 10 ) × 11 × 10 ℃ × 70.0° ≅ 2 × 10
4. (a) How many atoms of helium gas fill a balloon of diameter 30.0 cm at 20.0°C and 1.00 atm? (b)
What is the average kinetic energy of the helium atoms? (c) What is the root-mean-square speed
of each helium atom?
Solution
a. We know that the ideal gas law can be written as
= ,

2. = =
. × / × ( . )
. × ×
= 3.5418 × 10
b. The average kinetic energy can be obtained using . .=
That is,
c. = ,
We need to find the mass of a helium atom,
That is
= =
. /
. × /
= 6.64 × 10 /
= = 1.35 km/sec
5. A cube 10.0 cm on each edge contains air (with equivalent molar mass 28.9 g/mol) at atmospheric
pressure and temperature 300 K. Find (a) the mass of the gas, (b) its weight, and (c) the force it
exerts on each face of the cube. (d) Comment on the underlying physical reason why such a small
sample can exert such a great force.
Solution:
= → =
= = =
1.013 ×
10
× (0.1) × 2.89 ×
10
8.314( . ) × 300
= 1.17 × 10
The mass of the gas is 1.17 grams
Its weight is = = 1.17 × 10 × 10 = 11.7
The force exerted on the walls of the cube is
= = 1.013 ×
10
× 0.1 = 1013
The molecules to exert such a force on the walls have to have a high speed to hit the walls so hard.
6. A clock with a brass pendulum has a period of 1.000 s at 20.0°C. If the temperature increases to
30.0°C, (a) by how much does the period change, and (b) how much time does the clock gain or
lose in one week?
Solution:
The time period of the pendulum is given by

3. = 2
We need to find the pendulum length to make one oscillation in one second, that is
=
4
=
(1 ) × (9.80 / )
4
= 0.24824
Now, we know that the length of the pendulum is going to change because of temperature
change! Thus,
= (1 + ∆ ) = 0.24824 (1 + 19.0 × 10 ℃ × (30 − 20)℃) = 0.248287
= 2 = 2
0.248287
9.8
= 1.000101
The clock a little bit sluggish, it takes more than one second in each pendulum revolution! This
means the clock is going to delay behind other clocks per second by
∆ = 1.01 × 10
In one week, the clock is running behind by,
( ) = 7 ×
86400
×
1.01 × 10 sec
1
= 61.0848
The clock is going to delay almost a minute per week!
7. The temperature of a silver bar rises by 10.0°C when it absorbs 1.23 kJ of energy by heat. The
mass of the bar is 525 g. Determine the specific heat of silver.
Solution:
= ∆ → =
∆
=
1.23 × 10
0.525 × 10℃
= 234.28
8. A glass window pane has an area of 3.00 and a thickness of 0.600 cm. If the temperature
difference between its surfaces is 25.0°C, what is the rate of energy transfer by conduction
through the window?
Solution:
=
Δ
= 0.8 × 3.0
25.0
0.6 × 10
= 10
JGood Luck J
Hassan Ashour