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Physics

Heat

Easy

Question

The molecules of a given mass of a gas have a ‘rms’ velocity of 200 m/sec at 27⁰C and 1.0 x 10⁵ N/m² pressure. When the temperature is 127⁰C and pressure is 0.5 x10⁵ N/m² , the ‘rms‘ velocity in m/sec will be

$\frac{100 \sqrt{2}}{3}$
$100 \sqrt{2}$
$\frac{400}{\sqrt{3}}$
400

The correct answer is: $fraction numerator 400 over denominator square root of 3 end fraction$

$straight v subscript r m s end subscript equals square root of fraction numerator 3 R T over denominator M end fraction end root not stretchy rightwards double arrow straight v subscript r m s end subscript proportional to square root of T$

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$Five space identical space rods space are space joined space as space shown space in space figure. space Point space straight A space and space straight C space are space maintained space at space space temperature space 120 degree straight C space and space 20 degree straight C space respectively. space The space temperature space of space junction space straight B space will space be space$

$Five space identical space rods space are space joined space as space shown space in space figure. space Point space straight A space and space straight C space are space maintained space at space space temperature space 120 degree straight C space and space 20 degree straight C space respectively. space The space temperature space of space junction space straight B space will space be space$

parallel

$There space are space two space spherical space balls space straight A space and space straight B space of space the space same space material space with space same space surface comma space but space the space space diameter space of space straight A space is space half space that space of space straight B. space If space straight A space and space straight B space are space heated space to space the space same space temperature space and space space then space allowed space to space cool comma space then$

$There space are space two space spherical space balls space straight A space and space straight B space of space the space same space material space with space same space surface comma space but space the space space diameter space of space straight A space is space half space that space of space straight B. space If space straight A space and space straight B space are space heated space to space the space same space temperature space and space space then space allowed space to space cool comma space then$

$The space wavelength space of space maximum space intensity space of space radiation space emitted space by space straight a space star space is space 289.8 space nm. space The space space radiation space intensity space for space the space star space is space colon space left parenthesis Stefan ’ straight s space constant space 5.67 cross times 10 to the power of negative 8 end exponent Wm to the power of negative 2 end exponent straight K to the power of negative 4 end exponent space comma space constant space straight b equals space 2898 space straight mu mK right parenthesis$

$The space wavelength space of space maximum space intensity space of space radiation space emitted space by space straight a space star space is space 289.8 space nm. space The space space radiation space intensity space for space the space star space is space colon space left parenthesis Stefan ’ straight s space constant space 5.67 cross times 10 to the power of negative 8 end exponent Wm to the power of negative 2 end exponent straight K to the power of negative 4 end exponent space comma space constant space straight b equals space 2898 space straight mu mK right parenthesis$

$If space at space temperature space straight T subscript 1 equals 1000 straight K space space the space wavelength space is space 1.4 cross times 10 to the power of negative 6 end exponent straight m comma space space then space at space what space temperature space the space space wavelength space will space be space 2.8 cross times 10 to the power of negative 6 end exponent straight m space space space$

$If space at space temperature space straight T subscript 1 equals 1000 straight K space space the space wavelength space is space 1.4 cross times 10 to the power of negative 6 end exponent straight m comma space space then space at space what space temperature space the space space wavelength space will space be space 2.8 cross times 10 to the power of negative 6 end exponent straight m space space space$

parallel

$Wein apostrophe straight s space constant space is space 2892 cross times 10 to the power of negative 6 end exponent space space MKS space unit space and space the space value space of space straight lambda subscript straight m space space from space moon space is space 14.46 space microns. space What space is space the space surface space temperature space of space moon$

$Wein apostrophe straight s space constant space is space 2892 cross times 10 to the power of negative 6 end exponent space space MKS space unit space and space the space value space of space straight lambda subscript straight m space space from space moon space is space 14.46 space microns. space What space is space the space surface space temperature space of space moon$

$The space two space opposite space faces space of space straight a space cubical space piece space of space iron space left parenthesis thermal space conductivity space equals space 0.2 space CGS space units right parenthesis are space at space 100 to the power of degree straight C space space and space 0 to the power of degree straight C space in space ice. space If space the space area space of space straight a space surfaces space is space 4 cm squared space comma space then space the space mass space of space ice melted space in space 10 space minutes space will space be$

$The space two space opposite space faces space of space straight a space cubical space piece space of space iron space left parenthesis thermal space conductivity space equals space 0.2 space CGS space units right parenthesis are space at space 100 to the power of degree straight C space space and space 0 to the power of degree straight C space in space ice. space If space the space area space of space straight a space surfaces space is space 4 cm squared space comma space then space the space mass space of space ice melted space in space 10 space minutes space will space be$

$Four space rods space of space silver comma space copper comma space brass space and space wood space are space of space same space shape. space They space are space heated space together space after space wrapping space straight a space paper space on space it comma space the space paper space will space burn space first space on$

$Four space rods space of space silver comma space copper comma space brass space and space wood space are space of space same space shape. space They space are space heated space together space after space wrapping space straight a space paper space on space it comma space the space paper space will space burn space first space on$

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