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Standard XII

Physics

Ideal Gas Equation from KTG

If temperatur...

Question

If temperature of the atmosphere varies with height as $T = (T_{0} - a h)$ , where $a$ and $T_{0}$ positive constants, then find pressure as a function of height $(h)$ . Assume atmospheric pressure at sea level $(h = 0)$ is $p_{0}$ and molecular mass $M$ of the air and acceleration due to gravity $g$ to be constant :

P = P_{0} {(\frac{T_{0} - a h}{T_{0}})}^{M g / R a}

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P = P_{0} {(\frac{T_{0} - a h}{T_{0}})}^{2 M g / R a}

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P = P_{0} {(\frac{T_{0} - a h}{T_{0}})}^{3 M g / R a}

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P = P_{0} {(\frac{T_{0} - a h}{T_{0}})}^{4 M g / R a}

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Solution

The correct option is A $P = P_{0} {(\frac{T_{0} - a h}{T_{0}})}^{M g / R a}$

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If temperature of the atmosphere varies with height as T=(T0−ah), where a and T0 positive constants, then find pressure as a function of height (h). Assume atmospheric pressure at sea level (h=0) is p0 and molecular mass M of the air and acceleration due to gravity g to be constant :

The correct option is A P=P0(T0−ahT0)Mg/Ra

The correct option is A $P = P_{0} {(\frac{T_{0} - a h}{T_{0}})}^{M g / R a}$