Interpretation:
A derivative with respect to the same variable can be taken more than once:
and is called the second derivative of F. The following expressions are to be evaluated, assuming the
Concept introduction:
Slope of a line is defined as both direction and the steepness of the line. The value of slope is denoted by the letter ‘m’. In a straight-line equation y = mx + c, the slope is ‘m’. Generally, the slope of a line is calculated by finding the ratio of the vertical change to the horizontal change between two distinct points. The ideal gas law or general gas equation is the equation of state of a hypothetical ideal gas. The term was first coined by Emile Clapeyron in the year of 1834 as combination of other laws. The ideal gas law can be written as PV = nRT.
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Physical Chemistry
- What is the ratio of vrms/vmostprob for any gas at a given temperature?arrow_forwardRepeat the previous exercise for a gas that follows the Berthelot equation of state see exercise 1.55.arrow_forwardPerform a units analysis on the exponent of the barometric function and verify that the overall exponent is unitless.arrow_forward
- Interstellar space can be considered as having 10atoms of hydrogen per cubic centimeter and an average temperature far away from stars of 2.7K. Determine a the pressure of hydrogen in interstellar space and b the average speed of the hydrogen atoms. Compare these answers with values under normal Earth conditions.arrow_forwardAt what temperature (C) will 0.810mol of chlorine in a 15.7L vessel exert a pressure of 756torr?arrow_forwardThe previous exercise gives an expression for sound, the speed of sound in a gas. Determine the ratios sound/rms, sound/mostprob, and sound/. Which, if any, of these ratios is less than one? What are the physical interpretations of these ratios?arrow_forward
- For the following function, evaluate the derivatives in a-f below. F(w,x,y,z)=3xy2+w3z332yxy2z3w a.(Fx)w.y,zb.(Fw)x,y,zc.(Fy)w.x,zd.[ z(Fw)w.y,z ]w,y,ze.[ z(Fw)w.x,y ]w,y,zf.{ [ z(Fw)w.x,y ]w,y,z }x,y,zarrow_forwardIf relativistic effects were ignored, what temperature is required for hydrogen atoms to have an rms-average speed of 3.00108m/s? What do you think is the potential for actually achieving this temperature?arrow_forwardReferring to exercises 1.6 and 1.7, does it matter if the pressure difference is caused by an ideal gas or a non-ideal gas? Explain your answer.arrow_forward
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