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Mathematics
Problem
When the gas bubble is at a height
y
y
y
from the bottom, its temperature is – a.
T
0
(
P
0
+
ρ
ℓ
g
H
P
0
+
ρ
ℓ
g
y
)
2
/
5
T_0 \left( \frac{P_0 + \rho_\ell gH}{P_0 + \rho_\ell gy} \right)^{2/5}
T
0
(
P
0
+
ρ
ℓ
g
y
P
0
+
ρ
ℓ
g
H
)
2/5
b.
T
0
(
P
0
+
ρ
ℓ
g
(
H
−
y
)
P
0
+
ρ
ℓ
g
H
)
2
/
5
T_0 \left( \frac{P_0 + \rho_\ell g(H-y)}{P_0 + \rho_\ell gH} \right)^{2/5}
T
0
(
P
0
+
ρ
ℓ
g
H
P
0
+
ρ
ℓ
g
(
H
−
y
)
)
2/5
c.
T
0
(
P
0
+
ρ
ℓ
g
H
P
0
+
ρ
ℓ
g
y
)
3
/
5
T_0 \left( \frac{P_0 + \rho_\ell gH}{P_0 + \rho_\ell gy} \right)^{3/5}
T
0
(
P
0
+
ρ
ℓ
g
y
P
0
+
ρ
ℓ
g
H
)
3/5
d.
T
0
(
P
0
+
ρ
ℓ
g
(
H
−
y
)
P
0
+
ρ
ℓ
g
H
)
3
/
5
T_0 \left( \frac{P_0 + \rho_\ell g(H-y)}{P_0 + \rho_\ell gH} \right)^{3/5}
T
0
(
P
0
+
ρ
ℓ
g
H
P
0
+
ρ
ℓ
g
(
H
−
y
)
)
3/5
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