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An ideal gas expands according to the law P^2V=constant. The internal energy of the gas-(1) Increase continuously, (2) Decrease continuously, (3) Remains constant, (4) First increase and then decrease.

Asked by patra04011965 | 19 Mar, 2019, 01:19: AM

Expert Answer

Given,

P²V = constant

So,

P²V = k

Thus,

P squared equals k over V therefore P equals square root of fraction numerator k over denominator V space end fraction end root L e t space square root of k space equals space K T h u s comma P space equals space fraction numerator K over denominator square root of V end fraction... left parenthesis 1 right parenthesis N o w space w e space k n o w comma W equals space integral subscript V subscript 1 end subscript superscript V subscript 2 end superscript P. space d V therefore space W space equals K space integral subscript V subscript 1 end subscript superscript V subscript 2 end superscript fraction numerator K over denominator square root of V end fraction. space d V space... left parenthesis f r o m space left parenthesis 1 right parenthesis right parenthesis therefore space W space equals K space integral subscript V subscript 1 end subscript superscript V subscript 2 end superscript V to the power of negative bevelled 1 half end exponent. space d V space O n space i n t e g r a t i n g comma space w e space g e t comma therefore space W space equals space K space open square brackets fraction numerator V subscript 2 to the power of begin display style 1 half end style end exponent over denominator begin display style bevelled 1 half end style end fraction minus fraction numerator V subscript 1 to the power of begin display style 1 half end style end exponent over denominator begin display style bevelled 1 half end style end fraction close square brackets space equals space 2 K open square brackets square root of V subscript 2 end root minus space square root of V subscript 1 end root close square brackets

By first law of thermodynamics,

Δ U = Q + W

Q = 0

Δ U = Q + W

capital delta space U space equals space 2 K open square brackets square root of V subscript 2 end root space minus space square root of V subscript 1 end root close square brackets

So now, as the gas is expanding,

V₂ > V₁

Thus, Δ U will increase continuously.

Thus, correct option is (1)

Answered by Shiwani Sawant | 19 Mar, 2019, 12:55: PM

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