Verified Solution • 2025–26 Session moderate

QJEEAdv04Ph8eee: JEE Advanced 2004 Physics - Class 11 JEEAdv04Ph8eee Solution: Pressure depends on distance as, , where , are constants, z in…

Pressure depends on distance as, P=αβexp⁡(−αzkθ)P = {\alpha \over \beta }\exp \left( { - {{\alpha z} \over {k\theta }}} \right) , where α\alpha , β\beta are constants, z in distance, k is Boltzman's constant and θ\theta is temperature. The dimention of β\beta are

Multiple Choice Options

  • A [M0L0T0]
  • B [M-1L-1T-1]
  • C [M0L2T0]
  • D [M-1L1T2]

Step-by-Step Verified Solution

The given expression is

P=αβexp⁡(−αzkθ)P = {\alpha \over \beta }\exp \left( { - {{\alpha z} \over {k\theta }}} \right)

Now,

[z]=[L1][z] = [{L^1}]

[θ]=[K1][\theta ] = [{K^1}]

[k]=[M1L2T−2K−1][k] = [{M^1}{L^2}{T^{ - 2}}{K^{ - 1}}]

Since the terms which are raised to power in an exponential function are dimensionless, we get

[α]=[kθz]=[M1L1T−2][\alpha] = \left[ {{{k\theta } \over z}} \right] = [{M^1}{L^1}{T^{ - 2}}]

Also, [P]=[P] = [αβ]\left[ {{\alpha \over \beta }} \right]

⇒\Rightarrow [β]=[αP]\left[ \beta \right] = \left[ {{\alpha \over P}} \right]

⇒\Rightarrow [β]=[M1L1T−2ML−1T−2]\left[ \beta \right] = \left[ {{{{M^1}{L^1}{T^{ - 2}}} \over {M{L^{ - 1}}{T^{ - 2}}}}} \right] = [M0L2T0][{M^0}{L^2}{T^0}]

Answer (C)

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