physics : class11 Effect of Temperature on Surface Tension : Surface Tension : Properties of Bulk Matter MCQ Questions and Answers
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Effect of Temperature on Surface Tension
MCQ questions and answers.
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MCQ Questions
1. For a liquid whose surface tension obeys γ(T) = γ0[1 − α(T − T0)] over a limited temperature range, its surface tension becomes 20% of γ0 at what temperature rise above T0?
A.
0.2/α
B.
0.8/α
C.
1.2/α
D.
1/α
Correct Answer:
0.8/α
Explanation:
Putting γ(T) = 0.2γ0 in γ(T) = γ0[1 − α(T − T0)] gives 0.2 = 1 − αΔT, so αΔT = 0.8 and ΔT = 0.8/α.
2. A liquid has surface tension γ1 at temperature T1 and γ2 at temperature T2, with T2 > T1. If its surface tension varies linearly with temperature, which expression gives the fractional decrease in surface tension?
A.
(γ1 − γ2)/γ2
B.
(γ1 − γ2)/γ1
C.
(γ2 − γ1)/γ1
D.
(T2 − T1)/(γ1 − γ2)
Correct Answer:
(γ1 − γ2)/γ1
Explanation:
The fractional decrease is defined relative to the initial value γ1. Since surface tension decreases with temperature, it is (γ1 − γ2)/γ1.
3. A capillary tube is placed vertically in a liquid. If the temperature is increased slightly and the density change is neglected, what is the first-order fractional change in capillary rise h when γ decreases by 3%?
A.
An increase of 3%
B.
A decrease of 3%
C.
A decrease of 6%
D.
No change
Correct Answer:
A decrease of 3%
Explanation:
For a fixed capillary and contact angle, h = 2γ cosθ/(ρgr). With ρ unchanged, h is directly proportional to γ, so a 3% decrease in γ produces a 3% decrease in h.
4. At a certain temperature, the surface tension of a liquid is γ and its temperature coefficient is dγ/dT = −k. If the temperature rises by ΔT within the range where k is constant, the work required to create an additional surface area A changes by
A.
−kAΔT
B.
−γAΔT
C.
−kA
D.
−kΔT
Correct Answer:
−kAΔT
Explanation:
The surface work for area A is W = γA. A temperature increase changes surface tension by Δγ = (dγ/dT)ΔT = −kΔT. Therefore, the change in work is ΔW = AΔγ = −kAΔT.
5. Two soap bubbles have the same radius at temperatures T and T + ΔT, where ΔT > 0. If the surface tension decreases by 5% on heating, the excess pressure inside each bubble at T + ΔT is
A.
5% greater
B.
5% smaller
C.
10% smaller
D.
Unchanged
Correct Answer:
5% smaller
Explanation:
For a soap bubble, excess pressure is ΔP = 4γ/r. Since the radius is unchanged, the excess pressure is directly proportional to surface tension and therefore decreases by 5%.
6. The surface tension of a liquid is 0.072 N m⁻¹ at 20°C and decreases uniformly at 1.5 × 10⁻⁴ N m⁻¹ K⁻¹. At what temperature will its surface tension become 0.060 N m⁻¹?
A.
80°C
B.
90°C
C.
100°C
D.
120°C
Correct Answer:
100°C
Explanation:
The required decrease is 0.072 − 0.060 = 0.012 N m⁻¹. Thus ΔT = 0.012/(1.5 × 10⁻⁴) = 80 K. Starting from 20°C gives 100°C.
7. For a liquid in a capillary, h = 2γ cosθ/(ρgr). If heating causes γ to decrease by 2%, ρ to decrease by 1%, and θ and r to remain constant, the approximate fractional change in h is
A.
A decrease of 3%
B.
A decrease of 1%
C.
An increase of 1%
D.
An increase of 3%
Correct Answer:
A decrease of 1%
Explanation:
Since h is proportional to γ/ρ, the fractional change is Δh/h ≈ Δγ/γ − Δρ/ρ = (−2%) − (−1%) = −1%. Thus the capillary rise decreases by approximately 1%.
8. A liquid's surface tension is modeled by γ = γ0(1 − T/Tc), where Tc is its critical temperature and γ0 is constant. At what fraction of Tc is γ equal to one-half of γ0?
A.
T/Tc = 1/4
B.
T/Tc = 1/2
C.
T/Tc = 2/3
D.
T/Tc = 3/4
Correct Answer:
T/Tc = 1/2
Explanation:
Setting γ = γ0/2 gives 1 − T/Tc = 1/2, so T/Tc = 1/2. The model also shows that surface tension approaches zero as T approaches Tc.
9. A liquid has surface tension γ1 at T1 and γ2 at T2, with γ2 < γ1. Assuming a constant temperature coefficient over this interval, which quantity represents the magnitude of the temperature coefficient of surface tension?
A.
(γ1 + γ2)/(T2 − T1)
B.
(γ1 − γ2)/(T2 − T1)
C.
(T2 − T1)/(γ1 − γ2)
D.
(γ1γ2)/(T2 − T1)
Correct Answer:
(γ1 − γ2)/(T2 − T1)
Explanation:
The temperature coefficient is dγ/dT, which is negative because surface tension decreases with temperature. Its magnitude over the interval is |Δγ/ΔT| = (γ1 − γ2)/(T2 − T1).
10. At the same temperature, a liquid surface has surface tension γ and a soap solution has surface tension γ/2. If both are heated through the same temperature interval and each has the same fractional decrease in surface tension, what is the ratio of their decreases in surface tension?
A.
1:2
B.
2:1
C.
1:1
D.
1:4
Correct Answer:
2:1
Explanation:
For the same fractional decrease, the absolute decrease is proportional to the initial surface tension. The decreases are fγ and f(γ/2), giving the ratio fγ : fγ/2 = 2:1.
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